# QMBL - the Quantum Many-Body Leaderboard

> The best published variational ground-state energies for 322 lattice Hamiltonian instances (813 energies, 182 with a record). Read-only, generated from the repository's data/ directory, Apache-2.0.

Every row is one published claim about one Hamiltonian instance and carries the energy, its
error bar, the method, the primary reference, and a `bound_type`: strict variational bound,
projected/fixed-node estimate, zero-variance extrapolation, or numerically exact. Only strict
variational bounds can hold a record. Energies are stored as totals in VarBench's convention
and quoted per site; the conversion is in DATA.md. Individual energies must be cited to the
primary paper named on the row, not to this site.

## Pages
- [Leaderboard](https://qmbl.org/): the frontier instances, records and closest challengers.
- [All instances](https://qmbl.org/instances/): every one of the 322 instances, with its record.
- [Rules](https://qmbl.org/rules/): what counts as a record, ties, provenance, objections.
- [Data](https://qmbl.org/data/): row format, units and conventions, error metrics, defects.
- [Contribute](https://qmbl.org/contribute/): corrections, missing results, missing error bars.

## Data
- [Full dump](https://qmbl.org/api/qmbl.json): every instance and row in one JSON file.
- [Instance index](https://qmbl.org/api/instances.json): id, label, URL and record per instance.
- [Summary](https://qmbl.org/api/summary.json): the counts behind the headline numbers.
- [Repository](https://github.com/tzerweck/quantum-many-body-leaderboard): source data, build scripts, rules.
- Citation: https://doi.org/10.5281/zenodo.22753734 (concept DOI, always the latest release).

## Instances
- [chain, 20 sites, open](https://qmbl.org/i/Heisenberg/chain_20_O/): Heisenberg/chain_20_O, 5 energies, JSON at https://qmbl.org/api/i/Heisenberg/chain_20_O.json.
- [chain, 20 sites](https://qmbl.org/i/Heisenberg/chain_20_P/): Heisenberg/chain_20_P, 7 energies, JSON at https://qmbl.org/api/i/Heisenberg/chain_20_P.json.
- [chain, 200 sites, open](https://qmbl.org/i/Heisenberg/chain_200_O/): Heisenberg/chain_200_O, 3 energies, JSON at https://qmbl.org/api/i/Heisenberg/chain_200_O.json.
- [chain, 200 sites](https://qmbl.org/i/Heisenberg/chain_200_P/): Heisenberg/chain_200_P, 4 energies, JSON at https://qmbl.org/api/i/Heisenberg/chain_200_P.json.
- [kagome-24, 24 sites](https://qmbl.org/i/Heisenberg/kagome-24_24_P/): Heisenberg/kagome-24_24_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/kagome-24_24_P.json.
- [kagome 2x2 (12 sites)](https://qmbl.org/i/Heisenberg/kagome-2x2_12_P/): Heisenberg/kagome-2x2_12_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/kagome-2x2_12_P.json.
- [kagome 2x3 (18 sites)](https://qmbl.org/i/Heisenberg/kagome-2x3_18_P/): Heisenberg/kagome-2x3_18_P, 5 energies, JSON at https://qmbl.org/api/i/Heisenberg/kagome-2x3_18_P.json.
- [kagome-30, 30 sites](https://qmbl.org/i/Heisenberg/kagome-30_30_P/): Heisenberg/kagome-30_30_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/kagome-30_30_P.json.
- [kagome-36a, 36 sites](https://qmbl.org/i/Heisenberg/kagome-36a_36_P/): Heisenberg/kagome-36a_36_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/kagome-36a_36_P.json.
- [kagome-36b, 36 sites](https://qmbl.org/i/Heisenberg/kagome-36b_36_P/): Heisenberg/kagome-36b_36_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/kagome-36b_36_P.json.
- [kagome-36c, 36 sites](https://qmbl.org/i/Heisenberg/kagome-36c_36_P/): Heisenberg/kagome-36c_36_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/kagome-36c_36_P.json.
- [kagome-36d, 36 sites](https://qmbl.org/i/Heisenberg/kagome-36d_36_P/): Heisenberg/kagome-36d_36_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/kagome-36d_36_P.json.
- [kagome-42a, 42 sites](https://qmbl.org/i/Heisenberg/kagome-42a_42_P/): Heisenberg/kagome-42a_42_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/kagome-42a_42_P.json.
- [kagome-42b, 42 sites](https://qmbl.org/i/Heisenberg/kagome-42b_42_P/): Heisenberg/kagome-42b_42_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/kagome-42b_42_P.json.
- [kagome 4x4 (48 sites)](https://qmbl.org/i/Heisenberg/kagome-4x4_48_P/): Heisenberg/kagome-4x4_48_P, 4 energies, JSON at https://qmbl.org/api/i/Heisenberg/kagome-4x4_48_P.json.
- [kagome 6x6 (108 sites)](https://qmbl.org/i/Heisenberg/kagome-6x6_108_P/): Heisenberg/kagome-6x6_108_P, 2 energies, JSON at https://qmbl.org/api/i/Heisenberg/kagome-6x6_108_P.json.
- [kagome 8x8 (192 sites)](https://qmbl.org/i/Heisenberg/kagome-8x8_192_P/): Heisenberg/kagome-8x8_192_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/kagome-8x8_192_P.json.
- [pyrochlore 2x2x2 (128 sites)](https://qmbl.org/i/Heisenberg/pyrochlore-2x2x2_128_P/): Heisenberg/pyrochlore-2x2x2_128_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/pyrochlore-2x2x2_128_P.json.
- [pyrochlore 2x2x2 (32 sites)](https://qmbl.org/i/Heisenberg/pyrochlore-2x2x2_32_P/): Heisenberg/pyrochlore-2x2x2_32_P, 3 energies, JSON at https://qmbl.org/api/i/Heisenberg/pyrochlore-2x2x2_32_P.json.
- [pyrochlore 3x3x3 (108 sites)](https://qmbl.org/i/Heisenberg/pyrochlore-3x3x3_108_P/): Heisenberg/pyrochlore-3x3x3_108_P, 3 energies, JSON at https://qmbl.org/api/i/Heisenberg/pyrochlore-3x3x3_108_P.json.
- [pyrochlore 3x3x3 (432 sites)](https://qmbl.org/i/Heisenberg/pyrochlore-3x3x3_432_P/): Heisenberg/pyrochlore-3x3x3_432_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/pyrochlore-3x3x3_432_P.json.
- [pyrochlore 4x4x4 (1024 sites)](https://qmbl.org/i/Heisenberg/pyrochlore-4x4x4_1024_P/): Heisenberg/pyrochlore-4x4x4_1024_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/pyrochlore-4x4x4_1024_P.json.
- [pyrochlore 4x4x4 (256 sites)](https://qmbl.org/i/Heisenberg/pyrochlore-4x4x4_256_P/): Heisenberg/pyrochlore-4x4x4_256_P, 2 energies, JSON at https://qmbl.org/api/i/Heisenberg/pyrochlore-4x4x4_256_P.json.
- [rectangular 10x20, periodic/open](https://qmbl.org/i/Heisenberg/rectangular-10x20_200_PO/): Heisenberg/rectangular-10x20_200_PO, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/rectangular-10x20_200_PO.json.
- [rectangular 12x24, periodic/open](https://qmbl.org/i/Heisenberg/rectangular-12x24_288_PO/): Heisenberg/rectangular-12x24_288_PO, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/rectangular-12x24_288_PO.json.
- [rectangular 14x28, periodic/open](https://qmbl.org/i/Heisenberg/rectangular-14x28_392_PO/): Heisenberg/rectangular-14x28_392_PO, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/rectangular-14x28_392_PO.json.
- [rectangular 16x32, periodic/open](https://qmbl.org/i/Heisenberg/rectangular-16x32_512_PO/): Heisenberg/rectangular-16x32_512_PO, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/rectangular-16x32_512_PO.json.
- [rectangular 18x36, periodic/open](https://qmbl.org/i/Heisenberg/rectangular-18x36_648_PO/): Heisenberg/rectangular-18x36_648_PO, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/rectangular-18x36_648_PO.json.
- [rectangular 20x40, periodic/open](https://qmbl.org/i/Heisenberg/rectangular-20x40_800_PO/): Heisenberg/rectangular-20x40_800_PO, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/rectangular-20x40_800_PO.json.
- [rectangular 24x48, periodic/open](https://qmbl.org/i/Heisenberg/rectangular-24x48_1152_PO/): Heisenberg/rectangular-24x48_1152_PO, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/rectangular-24x48_1152_PO.json.
- [rectangular 32x64, periodic/open](https://qmbl.org/i/Heisenberg/rectangular-32x64_2048_PO/): Heisenberg/rectangular-32x64_2048_PO, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/rectangular-32x64_2048_PO.json.
- [rectangular 48x96, periodic/open](https://qmbl.org/i/Heisenberg/rectangular-48x96_4608_PO/): Heisenberg/rectangular-48x96_4608_PO, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/rectangular-48x96_4608_PO.json.
- [rectangular 4x8, periodic/open](https://qmbl.org/i/Heisenberg/rectangular-4x8_32_PO/): Heisenberg/rectangular-4x8_32_PO, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/rectangular-4x8_32_PO.json.
- [rectangular 64x128, periodic/open](https://qmbl.org/i/Heisenberg/rectangular-64x128_8192_PO/): Heisenberg/rectangular-64x128_8192_PO, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/rectangular-64x128_8192_PO.json.
- [rectangular 6x12, periodic/open](https://qmbl.org/i/Heisenberg/rectangular-6x12_72_PO/): Heisenberg/rectangular-6x12_72_PO, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/rectangular-6x12_72_PO.json.
- [rectangular 6x8](https://qmbl.org/i/Heisenberg/rectangular-6x8_48_P/): Heisenberg/rectangular-6x8_48_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/rectangular-6x8_48_P.json.
- [rectangular 8x16, periodic/open](https://qmbl.org/i/Heisenberg/rectangular-8x16_128_PO/): Heisenberg/rectangular-8x16_128_PO, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/rectangular-8x16_128_PO.json.
- [shuriken, 216 sites](https://qmbl.org/i/Heisenberg/shuriken_216_P/): Heisenberg/shuriken_216_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/shuriken_216_P.json.
- [shuriken, 24 sites](https://qmbl.org/i/Heisenberg/shuriken_24_P/): Heisenberg/shuriken_24_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/shuriken_24_P.json.
- [shuriken, 384 sites](https://qmbl.org/i/Heisenberg/shuriken_384_P/): Heisenberg/shuriken_384_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/shuriken_384_P.json.
- [shuriken, 96 sites](https://qmbl.org/i/Heisenberg/shuriken_96_P/): Heisenberg/shuriken_96_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/shuriken_96_P.json.
- [square 10x10, open](https://qmbl.org/i/Heisenberg/square_100_O/): Heisenberg/square_100_O, 16 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_100_O.json.
- [square 10x10](https://qmbl.org/i/Heisenberg/square_100_P/): Heisenberg/square_100_P, 12 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_100_P.json.
- [square 32x32, open](https://qmbl.org/i/Heisenberg/square_1024_O/): Heisenberg/square_1024_O, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_1024_O.json.
- [square 32x32](https://qmbl.org/i/Heisenberg/square_1024_P/): Heisenberg/square_1024_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_1024_P.json.
- [square 36x36](https://qmbl.org/i/Heisenberg/square_1296_P/): Heisenberg/square_1296_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_1296_P.json.
- [square 12x12, open](https://qmbl.org/i/Heisenberg/square_144_O/): Heisenberg/square_144_O, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_144_O.json.
- [square 12x12](https://qmbl.org/i/Heisenberg/square_144_P/): Heisenberg/square_144_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_144_P.json.
- [square 4x4](https://qmbl.org/i/Heisenberg/square_16_P/): Heisenberg/square_16_P, 3 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_16_P.json.
- [square 40x40](https://qmbl.org/i/Heisenberg/square_1600_P/): Heisenberg/square_1600_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_1600_P.json.
- [square 128x128, open](https://qmbl.org/i/Heisenberg/square_16384_O/): Heisenberg/square_16384_O, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_16384_O.json.
- [square 44x44](https://qmbl.org/i/Heisenberg/square_1936_P/): Heisenberg/square_1936_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_1936_P.json.
- [square 14x14, open](https://qmbl.org/i/Heisenberg/square_196_O/): Heisenberg/square_196_O, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_196_O.json.
- [square 14x14](https://qmbl.org/i/Heisenberg/square_196_P/): Heisenberg/square_196_P, 5 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_196_P.json.
- [square 48x48, open](https://qmbl.org/i/Heisenberg/square_2304_O/): Heisenberg/square_2304_O, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_2304_O.json.
- [square 48x48](https://qmbl.org/i/Heisenberg/square_2304_P/): Heisenberg/square_2304_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_2304_P.json.
- [square 16x16, open](https://qmbl.org/i/Heisenberg/square_256_O/): Heisenberg/square_256_O, 4 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_256_O.json.
- [square 16x16](https://qmbl.org/i/Heisenberg/square_256_P/): Heisenberg/square_256_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_256_P.json.
- [square 52x52](https://qmbl.org/i/Heisenberg/square_2704_P/): Heisenberg/square_2704_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_2704_P.json.
- [square 56x56](https://qmbl.org/i/Heisenberg/square_3136_P/): Heisenberg/square_3136_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_3136_P.json.
- [square 18x18, open](https://qmbl.org/i/Heisenberg/square_324_O/): Heisenberg/square_324_O, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_324_O.json.
- [square 18x18](https://qmbl.org/i/Heisenberg/square_324_P/): Heisenberg/square_324_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_324_P.json.
- [square 6x6, open](https://qmbl.org/i/Heisenberg/square_36_O/): Heisenberg/square_36_O, 5 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_36_O.json.
- [square 6x6](https://qmbl.org/i/Heisenberg/square_36_P/): Heisenberg/square_36_P, 9 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_36_P.json.
- [square 60x60](https://qmbl.org/i/Heisenberg/square_3600_P/): Heisenberg/square_3600_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_3600_P.json.
- [square, 40 sites](https://qmbl.org/i/Heisenberg/square_40_P/): Heisenberg/square_40_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_40_P.json.
- [square 20x20, open](https://qmbl.org/i/Heisenberg/square_400_O/): Heisenberg/square_400_O, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_400_O.json.
- [square 20x20](https://qmbl.org/i/Heisenberg/square_400_P/): Heisenberg/square_400_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_400_P.json.
- [square 64x64, open](https://qmbl.org/i/Heisenberg/square_4096_O/): Heisenberg/square_4096_O, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_4096_O.json.
- [square 64x64](https://qmbl.org/i/Heisenberg/square_4096_P/): Heisenberg/square_4096_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_4096_P.json.
- [square 22x22, open](https://qmbl.org/i/Heisenberg/square_484_O/): Heisenberg/square_484_O, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_484_O.json.
- [square 22x22](https://qmbl.org/i/Heisenberg/square_484_P/): Heisenberg/square_484_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_484_P.json.
- [square, 50 sites](https://qmbl.org/i/Heisenberg/square_50_P/): Heisenberg/square_50_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_50_P.json.
- [square 72x72](https://qmbl.org/i/Heisenberg/square_5184_P/): Heisenberg/square_5184_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_5184_P.json.
- [square 24x24, open](https://qmbl.org/i/Heisenberg/square_576_O/): Heisenberg/square_576_O, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_576_O.json.
- [square 24x24](https://qmbl.org/i/Heisenberg/square_576_P/): Heisenberg/square_576_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_576_P.json.
- [square 8x8, open](https://qmbl.org/i/Heisenberg/square_64_O/): Heisenberg/square_64_O, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_64_O.json.
- [square 8x8](https://qmbl.org/i/Heisenberg/square_64_P/): Heisenberg/square_64_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_64_P.json.
- [square 80x80](https://qmbl.org/i/Heisenberg/square_6400_P/): Heisenberg/square_6400_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_6400_P.json.
- [square 26x26, open](https://qmbl.org/i/Heisenberg/square_676_O/): Heisenberg/square_676_O, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_676_O.json.
- [square 26x26](https://qmbl.org/i/Heisenberg/square_676_P/): Heisenberg/square_676_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_676_P.json.
- [square 88x88](https://qmbl.org/i/Heisenberg/square_7744_P/): Heisenberg/square_7744_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_7744_P.json.
- [square 28x28, open](https://qmbl.org/i/Heisenberg/square_784_O/): Heisenberg/square_784_O, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_784_O.json.
- [square 28x28](https://qmbl.org/i/Heisenberg/square_784_P/): Heisenberg/square_784_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_784_P.json.
- [square 30x30](https://qmbl.org/i/Heisenberg/square_900_P/): Heisenberg/square_900_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_900_P.json.
- [square 96x96, open](https://qmbl.org/i/Heisenberg/square_9216_O/): Heisenberg/square_9216_O, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_9216_O.json.
- [square 96x96](https://qmbl.org/i/Heisenberg/square_9216_P/): Heisenberg/square_9216_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/square_9216_P.json.
- [triangular 10x10, open](https://qmbl.org/i/Heisenberg/triangular_100_O/): Heisenberg/triangular_100_O, 7 energies, JSON at https://qmbl.org/api/i/Heisenberg/triangular_100_O.json.
- [triangular, 108 sites](https://qmbl.org/i/Heisenberg/triangular_108_P/): Heisenberg/triangular_108_P, 2 energies, JSON at https://qmbl.org/api/i/Heisenberg/triangular_108_P.json.
- [triangular 12x12, open](https://qmbl.org/i/Heisenberg/triangular_144_O/): Heisenberg/triangular_144_O, 5 energies, JSON at https://qmbl.org/api/i/Heisenberg/triangular_144_O.json.
- [triangular 12x12](https://qmbl.org/i/Heisenberg/triangular_144_P/): Heisenberg/triangular_144_P, 4 energies, JSON at https://qmbl.org/api/i/Heisenberg/triangular_144_P.json.
- [triangular 4x4](https://qmbl.org/i/Heisenberg/triangular_16_P/): Heisenberg/triangular_16_P, 5 energies, JSON at https://qmbl.org/api/i/Heisenberg/triangular_16_P.json.
- [triangular 14x14, open](https://qmbl.org/i/Heisenberg/triangular_196_O/): Heisenberg/triangular_196_O, 5 energies, JSON at https://qmbl.org/api/i/Heisenberg/triangular_196_O.json.
- [triangular 16x16, open](https://qmbl.org/i/Heisenberg/triangular_256_O/): Heisenberg/triangular_256_O, 4 energies, JSON at https://qmbl.org/api/i/Heisenberg/triangular_256_O.json.
- [triangular 6x6](https://qmbl.org/i/Heisenberg/triangular_36_P/): Heisenberg/triangular_36_P, 8 energies, JSON at https://qmbl.org/api/i/Heisenberg/triangular_36_P.json.
- [triangular, 48 sites](https://qmbl.org/i/Heisenberg/triangular_48_P/): Heisenberg/triangular_48_P, 1 energies, JSON at https://qmbl.org/api/i/Heisenberg/triangular_48_P.json.
- [chain, 14 sites, U = 1, n ≈ 0.5714](https://qmbl.org/i/Hubbard/chain_14_P_4_1/): Hubbard/chain_14_P_4_1, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/chain_14_P_4_1.json.
- [chain, 14 sites, U = 1.66810054, n ≈ 0.5714](https://qmbl.org/i/Hubbard/chain_14_P_4_1.66810054/): Hubbard/chain_14_P_4_1.66810054, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/chain_14_P_4_1.66810054.json.
- [chain, 14 sites, U = 10, n ≈ 0.5714](https://qmbl.org/i/Hubbard/chain_14_P_4_10/): Hubbard/chain_14_P_4_10, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/chain_14_P_4_10.json.
- [chain, 14 sites, U = 2.15443469, n ≈ 0.5714](https://qmbl.org/i/Hubbard/chain_14_P_4_2.15443469/): Hubbard/chain_14_P_4_2.15443469, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/chain_14_P_4_2.15443469.json.
- [chain, 14 sites, U = 2.7825594, n ≈ 0.5714](https://qmbl.org/i/Hubbard/chain_14_P_4_2.7825594/): Hubbard/chain_14_P_4_2.7825594, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/chain_14_P_4_2.7825594.json.
- [chain, 14 sites, U = 3.59381366, n ≈ 0.5714](https://qmbl.org/i/Hubbard/chain_14_P_4_3.59381366/): Hubbard/chain_14_P_4_3.59381366, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/chain_14_P_4_3.59381366.json.
- [chain, 14 sites, U = 4.64158882, n ≈ 0.5714](https://qmbl.org/i/Hubbard/chain_14_P_4_4.64158882/): Hubbard/chain_14_P_4_4.64158882, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/chain_14_P_4_4.64158882.json.
- [chain, 14 sites, U = 7.74263683, n ≈ 0.5714](https://qmbl.org/i/Hubbard/chain_14_P_4_7.74263683/): Hubbard/chain_14_P_4_7.74263683, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/chain_14_P_4_7.74263683.json.
- [rectangular 14x16, U = 8, n = 0.875](https://qmbl.org/i/Hubbard/rectangular-14x16_224_P_98_8/): Hubbard/rectangular-14x16_224_P_98_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-14x16_224_P_98_8.json.
- [rectangular 4x16, U = 8, n = 0.875](https://qmbl.org/i/Hubbard/rectangular-4x16_64_P_28_8/): Hubbard/rectangular-4x16_64_P_28_8, 8 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-4x16_64_P_28_8.json.
- [rectangular 4x16, periodic/open, U = 2, n = 0.8125](https://qmbl.org/i/Hubbard/rectangular-4x16_64_PO_26_2/): Hubbard/rectangular-4x16_64_PO_26_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-4x16_64_PO_26_2.json.
- [rectangular 4x16, periodic/open, U = 8, n = 0.8125](https://qmbl.org/i/Hubbard/rectangular-4x16_64_PO_26_8/): Hubbard/rectangular-4x16_64_PO_26_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-4x16_64_PO_26_8.json.
- [rectangular 4x16, periodic/open, U = 2, n = 0.875](https://qmbl.org/i/Hubbard/rectangular-4x16_64_PO_28_2/): Hubbard/rectangular-4x16_64_PO_28_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-4x16_64_PO_28_2.json.
- [rectangular 4x16, periodic/open, U = 8, n = 0.875](https://qmbl.org/i/Hubbard/rectangular-4x16_64_PO_28_8/): Hubbard/rectangular-4x16_64_PO_28_8, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-4x16_64_PO_28_8.json.
- [rectangular 4x16, periodic/open, U = 2, n = 0.9375](https://qmbl.org/i/Hubbard/rectangular-4x16_64_PO_30_2/): Hubbard/rectangular-4x16_64_PO_30_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-4x16_64_PO_30_2.json.
- [rectangular 4x16, periodic/open, U = 8, n = 0.9375](https://qmbl.org/i/Hubbard/rectangular-4x16_64_PO_30_8/): Hubbard/rectangular-4x16_64_PO_30_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-4x16_64_PO_30_8.json.
- [rectangular 4x16, periodic/open, U = 2, n = 1](https://qmbl.org/i/Hubbard/rectangular-4x16_64_PO_32_2/): Hubbard/rectangular-4x16_64_PO_32_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-4x16_64_PO_32_2.json.
- [rectangular 4x16, periodic/open, U = 8, n = 1](https://qmbl.org/i/Hubbard/rectangular-4x16_64_PO_32_8/): Hubbard/rectangular-4x16_64_PO_32_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-4x16_64_PO_32_8.json.
- [rectangular 4x8, U = 8, n = 0.875](https://qmbl.org/i/Hubbard/rectangular-4x8_32_P_14_8/): Hubbard/rectangular-4x8_32_P_14_8, 3 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-4x8_32_P_14_8.json.
- [rectangular 4x8, periodic/open, U = 8, n = 0.875](https://qmbl.org/i/Hubbard/rectangular-4x8_32_PO_14_8/): Hubbard/rectangular-4x8_32_PO_14_8, 4 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-4x8_32_PO_14_8.json.
- [rectangular 6x48, U = 8, n ≈ 0.8333](https://qmbl.org/i/Hubbard/rectangular-6x48_288_P_120_8/): Hubbard/rectangular-6x48_288_P_120_8, 4 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-6x48_288_P_120_8.json.
- [rectangular 6x48, U = 12, n = 0.875](https://qmbl.org/i/Hubbard/rectangular-6x48_288_P_126_12/): Hubbard/rectangular-6x48_288_P_126_12, 4 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-6x48_288_P_126_12.json.
- [rectangular 6x48, U = 8, n = 0.875](https://qmbl.org/i/Hubbard/rectangular-6x48_288_P_126_8/): Hubbard/rectangular-6x48_288_P_126_8, 4 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-6x48_288_P_126_8.json.
- [rectangular 6x48, U = 8, n ≈ 0.9167](https://qmbl.org/i/Hubbard/rectangular-6x48_288_P_132_8/): Hubbard/rectangular-6x48_288_P_132_8, 4 energies, JSON at https://qmbl.org/api/i/Hubbard/rectangular-6x48_288_P_132_8.json.
- [square 10x10, U = 4, n = 0.8](https://qmbl.org/i/Hubbard/square_100_P_40_4/): Hubbard/square_100_P_40_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_100_P_40_4.json.
- [square 10x10, U = 2, n = 1](https://qmbl.org/i/Hubbard/square_100_P_50_2/): Hubbard/square_100_P_50_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_100_P_50_2.json.
- [square 10x10, U = 4, n = 1](https://qmbl.org/i/Hubbard/square_100_P_50_4/): Hubbard/square_100_P_50_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_100_P_50_4.json.
- [square 10x10, U = 6, n = 1](https://qmbl.org/i/Hubbard/square_100_P_50_6/): Hubbard/square_100_P_50_6, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_100_P_50_6.json.
- [square 10x10, U = 8, n = 1](https://qmbl.org/i/Hubbard/square_100_P_50_8/): Hubbard/square_100_P_50_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_100_P_50_8.json.
- [square 10x10, periodic/antiperiodic, U = 2, n = 1](https://qmbl.org/i/Hubbard/square_100_PA_50_2/): Hubbard/square_100_PA_50_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_100_PA_50_2.json.
- [square 10x10, periodic/antiperiodic, U = 4, n = 1](https://qmbl.org/i/Hubbard/square_100_PA_50_4/): Hubbard/square_100_PA_50_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_100_PA_50_4.json.
- [square 10x10, periodic/antiperiodic, U = 6, n = 1](https://qmbl.org/i/Hubbard/square_100_PA_50_6/): Hubbard/square_100_PA_50_6, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_100_PA_50_6.json.
- [square 10x10, periodic/antiperiodic, U = 8, n = 1](https://qmbl.org/i/Hubbard/square_100_PA_50_8/): Hubbard/square_100_PA_50_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_100_PA_50_8.json.
- [square 12x12, U = 4, n ≈ 0.8056](https://qmbl.org/i/Hubbard/square_144_P_58_4/): Hubbard/square_144_P_58_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_144_P_58_4.json.
- [square 12x12, U = 2, n = 1](https://qmbl.org/i/Hubbard/square_144_P_72_2/): Hubbard/square_144_P_72_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_144_P_72_2.json.
- [square 12x12, U = 4, n = 1](https://qmbl.org/i/Hubbard/square_144_P_72_4/): Hubbard/square_144_P_72_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_144_P_72_4.json.
- [square 12x12, U = 6, n = 1](https://qmbl.org/i/Hubbard/square_144_P_72_6/): Hubbard/square_144_P_72_6, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_144_P_72_6.json.
- [square 12x12, U = 8, n = 1](https://qmbl.org/i/Hubbard/square_144_P_72_8/): Hubbard/square_144_P_72_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_144_P_72_8.json.
- [square 12x12, periodic/antiperiodic, U = 2, n = 1](https://qmbl.org/i/Hubbard/square_144_PA_72_2/): Hubbard/square_144_PA_72_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_144_PA_72_2.json.
- [square 12x12, periodic/antiperiodic, U = 4, n = 1](https://qmbl.org/i/Hubbard/square_144_PA_72_4/): Hubbard/square_144_PA_72_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_144_PA_72_4.json.
- [square 12x12, periodic/antiperiodic, U = 6, n = 1](https://qmbl.org/i/Hubbard/square_144_PA_72_6/): Hubbard/square_144_PA_72_6, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_144_PA_72_6.json.
- [square 12x12, periodic/antiperiodic, U = 8, n = 1](https://qmbl.org/i/Hubbard/square_144_PA_72_8/): Hubbard/square_144_PA_72_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_144_PA_72_8.json.
- [square 4x4, U = 10, n = 0.5](https://qmbl.org/i/Hubbard/square_16_P_4_10/): Hubbard/square_16_P_4_10, 3 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_4_10.json.
- [square 4x4, U = 2, n = 0.5](https://qmbl.org/i/Hubbard/square_16_P_4_2/): Hubbard/square_16_P_4_2, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_4_2.json.
- [square 4x4, U = 3.5981, n = 0.5](https://qmbl.org/i/Hubbard/square_16_P_4_3.5981/): Hubbard/square_16_P_4_3.5981, 3 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_4_3.5981.json.
- [square 4x4, U = 4, n = 0.5](https://qmbl.org/i/Hubbard/square_16_P_4_4/): Hubbard/square_16_P_4_4, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_4_4.json.
- [square 4x4, U = 6, n = 0.5](https://qmbl.org/i/Hubbard/square_16_P_4_6/): Hubbard/square_16_P_4_6, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_4_6.json.
- [square 4x4, U = 7.74264, n = 0.5](https://qmbl.org/i/Hubbard/square_16_P_4_7.74264/): Hubbard/square_16_P_4_7.74264, 3 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_4_7.74264.json.
- [square 4x4, U = 8, n = 0.5](https://qmbl.org/i/Hubbard/square_16_P_4_8/): Hubbard/square_16_P_4_8, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_4_8.json.
- [square 4x4, U = 10, n = 0.625](https://qmbl.org/i/Hubbard/square_16_P_5_10/): Hubbard/square_16_P_5_10, 3 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_5_10.json.
- [square 4x4, U = 2, n = 0.625](https://qmbl.org/i/Hubbard/square_16_P_5_2/): Hubbard/square_16_P_5_2, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_5_2.json.
- [square 4x4, U = 2.1544, n = 0.625](https://qmbl.org/i/Hubbard/square_16_P_5_2.1544/): Hubbard/square_16_P_5_2.1544, 3 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_5_2.1544.json.
- [square 4x4, U = 3.5981, n = 0.625](https://qmbl.org/i/Hubbard/square_16_P_5_3.5981/): Hubbard/square_16_P_5_3.5981, 3 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_5_3.5981.json.
- [square 4x4, U = 4, n = 0.625](https://qmbl.org/i/Hubbard/square_16_P_5_4/): Hubbard/square_16_P_5_4, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_5_4.json.
- [square 4x4, U = 6, n = 0.625](https://qmbl.org/i/Hubbard/square_16_P_5_6/): Hubbard/square_16_P_5_6, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_5_6.json.
- [square 4x4, U = 7.74264, n = 0.625](https://qmbl.org/i/Hubbard/square_16_P_5_7.74264/): Hubbard/square_16_P_5_7.74264, 3 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_5_7.74264.json.
- [square 4x4, U = 8, n = 0.625](https://qmbl.org/i/Hubbard/square_16_P_5_8/): Hubbard/square_16_P_5_8, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_5_8.json.
- [square 4x4, U = 2, n = 1](https://qmbl.org/i/Hubbard/square_16_P_8_2/): Hubbard/square_16_P_8_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_8_2.json.
- [square 4x4, U = 4, n = 1](https://qmbl.org/i/Hubbard/square_16_P_8_4/): Hubbard/square_16_P_8_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_8_4.json.
- [square 4x4, U = 6, n = 1](https://qmbl.org/i/Hubbard/square_16_P_8_6/): Hubbard/square_16_P_8_6, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_8_6.json.
- [square 4x4, U = 8, n = 1](https://qmbl.org/i/Hubbard/square_16_P_8_8/): Hubbard/square_16_P_8_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_P_8_8.json.
- [square 4x4, periodic/antiperiodic, U = 2, n = 1](https://qmbl.org/i/Hubbard/square_16_PA_8_2/): Hubbard/square_16_PA_8_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_PA_8_2.json.
- [square 4x4, periodic/antiperiodic, U = 4, n = 1](https://qmbl.org/i/Hubbard/square_16_PA_8_4/): Hubbard/square_16_PA_8_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_PA_8_4.json.
- [square 4x4, periodic/antiperiodic, U = 6, n = 1](https://qmbl.org/i/Hubbard/square_16_PA_8_6/): Hubbard/square_16_PA_8_6, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_PA_8_6.json.
- [square 4x4, periodic/antiperiodic, U = 8, n = 1](https://qmbl.org/i/Hubbard/square_16_PA_8_8/): Hubbard/square_16_PA_8_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_16_PA_8_8.json.
- [square 14x14, U = 2, n = 1](https://qmbl.org/i/Hubbard/square_196_P_98_2/): Hubbard/square_196_P_98_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_196_P_98_2.json.
- [square 14x14, U = 4, n = 1](https://qmbl.org/i/Hubbard/square_196_P_98_4/): Hubbard/square_196_P_98_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_196_P_98_4.json.
- [square 14x14, U = 6, n = 1](https://qmbl.org/i/Hubbard/square_196_P_98_6/): Hubbard/square_196_P_98_6, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_196_P_98_6.json.
- [square 14x14, U = 8, n = 1](https://qmbl.org/i/Hubbard/square_196_P_98_8/): Hubbard/square_196_P_98_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_196_P_98_8.json.
- [square 14x14, periodic/antiperiodic, U = 2, n = 1](https://qmbl.org/i/Hubbard/square_196_PA_98_2/): Hubbard/square_196_PA_98_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_196_PA_98_2.json.
- [square 14x14, periodic/antiperiodic, U = 4, n = 1](https://qmbl.org/i/Hubbard/square_196_PA_98_4/): Hubbard/square_196_PA_98_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_196_PA_98_4.json.
- [square 14x14, periodic/antiperiodic, U = 6, n = 1](https://qmbl.org/i/Hubbard/square_196_PA_98_6/): Hubbard/square_196_PA_98_6, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_196_PA_98_6.json.
- [square 14x14, periodic/antiperiodic, U = 8, n = 1](https://qmbl.org/i/Hubbard/square_196_PA_98_8/): Hubbard/square_196_PA_98_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_196_PA_98_8.json.
- [square 16x16, U = 8, n ≈ 0.8281](https://qmbl.org/i/Hubbard/square_256_P_106_8/): Hubbard/square_256_P_106_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_106_8.json.
- [square 16x16, U = 8, n ≈ 0.8438](https://qmbl.org/i/Hubbard/square_256_P_108_8/): Hubbard/square_256_P_108_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_108_8.json.
- [square 16x16, U = 8, n ≈ 0.8516](https://qmbl.org/i/Hubbard/square_256_P_109_8/): Hubbard/square_256_P_109_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_109_8.json.
- [square 16x16, U = 8, n ≈ 0.8594](https://qmbl.org/i/Hubbard/square_256_P_110_8/): Hubbard/square_256_P_110_8, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_110_8.json.
- [square 16x16, U = 8, n ≈ 0.8672](https://qmbl.org/i/Hubbard/square_256_P_111_8/): Hubbard/square_256_P_111_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_111_8.json.
- [square 16x16, U = -4, n = 0.875](https://qmbl.org/i/Hubbard/square_256_P_112_-4/): Hubbard/square_256_P_112_-4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_112_-4.json.
- [square 16x16, U = -8, n = 0.875](https://qmbl.org/i/Hubbard/square_256_P_112_-8/): Hubbard/square_256_P_112_-8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_112_-8.json.
- [square 16x16, U = 4, n = 0.875](https://qmbl.org/i/Hubbard/square_256_P_112_4/): Hubbard/square_256_P_112_4, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_112_4.json.
- [square 16x16, U = 6, n = 0.875](https://qmbl.org/i/Hubbard/square_256_P_112_6/): Hubbard/square_256_P_112_6, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_112_6.json.
- [square 16x16, U = 8, n = 0.875](https://qmbl.org/i/Hubbard/square_256_P_112_8/): Hubbard/square_256_P_112_8, 13 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_112_8.json.
- [square 16x16, U = 8, n ≈ 0.8828](https://qmbl.org/i/Hubbard/square_256_P_113_8/): Hubbard/square_256_P_113_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_113_8.json.
- [square 16x16, U = 4, n ≈ 0.8906](https://qmbl.org/i/Hubbard/square_256_P_114_4/): Hubbard/square_256_P_114_4, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_114_4.json.
- [square 16x16, U = 6, n ≈ 0.8906](https://qmbl.org/i/Hubbard/square_256_P_114_6/): Hubbard/square_256_P_114_6, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_114_6.json.
- [square 16x16, U = 8, n ≈ 0.8906](https://qmbl.org/i/Hubbard/square_256_P_114_8/): Hubbard/square_256_P_114_8, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_114_8.json.
- [square 16x16, U = 8, n ≈ 0.8984](https://qmbl.org/i/Hubbard/square_256_P_115_8/): Hubbard/square_256_P_115_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_115_8.json.
- [square 16x16, U = 8, n ≈ 0.9063](https://qmbl.org/i/Hubbard/square_256_P_116_8/): Hubbard/square_256_P_116_8, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_116_8.json.
- [square 16x16, U = 8, n ≈ 0.9141](https://qmbl.org/i/Hubbard/square_256_P_117_8/): Hubbard/square_256_P_117_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_117_8.json.
- [square 16x16, U = 8, n ≈ 0.9219](https://qmbl.org/i/Hubbard/square_256_P_118_8/): Hubbard/square_256_P_118_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_118_8.json.
- [square 16x16, U = 8, n = 0.9375](https://qmbl.org/i/Hubbard/square_256_P_120_8/): Hubbard/square_256_P_120_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_120_8.json.
- [square 16x16, U = -4, n = 1](https://qmbl.org/i/Hubbard/square_256_P_128_-4/): Hubbard/square_256_P_128_-4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_128_-4.json.
- [square 16x16, U = -8, n = 1](https://qmbl.org/i/Hubbard/square_256_P_128_-8/): Hubbard/square_256_P_128_-8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_128_-8.json.
- [square 16x16, U = 2, n = 1](https://qmbl.org/i/Hubbard/square_256_P_128_2/): Hubbard/square_256_P_128_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_128_2.json.
- [square 16x16, U = 4, n = 1](https://qmbl.org/i/Hubbard/square_256_P_128_4/): Hubbard/square_256_P_128_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_128_4.json.
- [square 16x16, U = 6, n = 1](https://qmbl.org/i/Hubbard/square_256_P_128_6/): Hubbard/square_256_P_128_6, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_128_6.json.
- [square 16x16, U = 8, n = 1](https://qmbl.org/i/Hubbard/square_256_P_128_8/): Hubbard/square_256_P_128_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_P_128_8.json.
- [square 16x16, periodic/antiperiodic, U = 8, n ≈ 0.8359](https://qmbl.org/i/Hubbard/square_256_PA_107_8/): Hubbard/square_256_PA_107_8, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_PA_107_8.json.
- [square 16x16, periodic/antiperiodic, U = 8, n ≈ 0.8359, t12](https://qmbl.org/i/Hubbard/square_256_PA_107_8_t12/): Hubbard/square_256_PA_107_8_t12, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_PA_107_8_t12.json.
- [square 16x16, periodic/antiperiodic, U = 8, n ≈ 0.8359, t12, UV1V2](https://qmbl.org/i/Hubbard/square_256_PA_107_8_t12_UV1V2/): Hubbard/square_256_PA_107_8_t12_UV1V2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_PA_107_8_t12_UV1V2.json.
- [square 16x16, periodic/antiperiodic, U = 2, n = 1](https://qmbl.org/i/Hubbard/square_256_PA_128_2/): Hubbard/square_256_PA_128_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_PA_128_2.json.
- [square 16x16, periodic/antiperiodic, U = 4, n = 1](https://qmbl.org/i/Hubbard/square_256_PA_128_4/): Hubbard/square_256_PA_128_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_PA_128_4.json.
- [square 16x16, periodic/antiperiodic, U = 6, n = 1](https://qmbl.org/i/Hubbard/square_256_PA_128_6/): Hubbard/square_256_PA_128_6, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_PA_128_6.json.
- [square 16x16, periodic/antiperiodic, U = 8, n = 1](https://qmbl.org/i/Hubbard/square_256_PA_128_8/): Hubbard/square_256_PA_128_8, 4 energies, JSON at https://qmbl.org/api/i/Hubbard/square_256_PA_128_8.json.
- [square 6x6, U = 4, n ≈ 0.6667](https://qmbl.org/i/Hubbard/square_36_P_12_4/): Hubbard/square_36_P_12_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_36_P_12_4.json.
- [square 6x6, U = 2, n = 1](https://qmbl.org/i/Hubbard/square_36_P_18_2/): Hubbard/square_36_P_18_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_36_P_18_2.json.
- [square 6x6, U = 4, n = 1](https://qmbl.org/i/Hubbard/square_36_P_18_4/): Hubbard/square_36_P_18_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_36_P_18_4.json.
- [square 6x6, U = 6, n = 1](https://qmbl.org/i/Hubbard/square_36_P_18_6/): Hubbard/square_36_P_18_6, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_36_P_18_6.json.
- [square 6x6, U = 8, n = 1](https://qmbl.org/i/Hubbard/square_36_P_18_8/): Hubbard/square_36_P_18_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_36_P_18_8.json.
- [square 6x6, U = 4, n ≈ 1.3333](https://qmbl.org/i/Hubbard/square_36_P_24_4/): Hubbard/square_36_P_24_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_36_P_24_4.json.
- [square 6x6, periodic/antiperiodic, U = 2, n = 1](https://qmbl.org/i/Hubbard/square_36_PA_18_2/): Hubbard/square_36_PA_18_2, 3 energies, JSON at https://qmbl.org/api/i/Hubbard/square_36_PA_18_2.json.
- [square 6x6, periodic/antiperiodic, U = 4, n = 1](https://qmbl.org/i/Hubbard/square_36_PA_18_4/): Hubbard/square_36_PA_18_4, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_36_PA_18_4.json.
- [square 6x6, periodic/antiperiodic, U = 6, n = 1](https://qmbl.org/i/Hubbard/square_36_PA_18_6/): Hubbard/square_36_PA_18_6, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_36_PA_18_6.json.
- [square 6x6, periodic/antiperiodic, U = 8, n = 1](https://qmbl.org/i/Hubbard/square_36_PA_18_8/): Hubbard/square_36_PA_18_8, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_36_PA_18_8.json.
- [square, 50 sites, U = 8, n = 0.84](https://qmbl.org/i/Hubbard/square_50_P_21_8/): Hubbard/square_50_P_21_8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_50_P_21_8.json.
- [square 8x8, U = 4, n = 0.4375](https://qmbl.org/i/Hubbard/square_64_P_14_4/): Hubbard/square_64_P_14_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_14_4.json.
- [square 8x8, U = 4, n = 0.6875](https://qmbl.org/i/Hubbard/square_64_P_22_4/): Hubbard/square_64_P_22_4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_22_4.json.
- [square 8x8, U = -4, n ≈ 0.7813](https://qmbl.org/i/Hubbard/square_64_P_25_-4/): Hubbard/square_64_P_25_-4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_25_-4.json.
- [square 8x8, U = -8, n ≈ 0.7813](https://qmbl.org/i/Hubbard/square_64_P_25_-8/): Hubbard/square_64_P_25_-8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_25_-8.json.
- [square 8x8, U = 4, n ≈ 0.7813](https://qmbl.org/i/Hubbard/square_64_P_25_4/): Hubbard/square_64_P_25_4, 3 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_25_4.json.
- [square 8x8, U = 8, n ≈ 0.7813](https://qmbl.org/i/Hubbard/square_64_P_25_8/): Hubbard/square_64_P_25_8, 3 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_25_8.json.
- [square 8x8, U = -4, n = 0.875](https://qmbl.org/i/Hubbard/square_64_P_28_-4/): Hubbard/square_64_P_28_-4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_28_-4.json.
- [square 8x8, U = -8, n = 0.875](https://qmbl.org/i/Hubbard/square_64_P_28_-8/): Hubbard/square_64_P_28_-8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_28_-8.json.
- [square 8x8, U = 4, n = 0.875](https://qmbl.org/i/Hubbard/square_64_P_28_4/): Hubbard/square_64_P_28_4, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_28_4.json.
- [square 8x8, U = 8, n = 0.875](https://qmbl.org/i/Hubbard/square_64_P_28_8/): Hubbard/square_64_P_28_8, 8 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_28_8.json.
- [square 8x8, U = -4, n = 1](https://qmbl.org/i/Hubbard/square_64_P_32_-4/): Hubbard/square_64_P_32_-4, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_32_-4.json.
- [square 8x8, U = -8, n = 1](https://qmbl.org/i/Hubbard/square_64_P_32_-8/): Hubbard/square_64_P_32_-8, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_32_-8.json.
- [square 8x8, U = 2, n = 1](https://qmbl.org/i/Hubbard/square_64_P_32_2/): Hubbard/square_64_P_32_2, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_32_2.json.
- [square 8x8, U = 4, n = 1](https://qmbl.org/i/Hubbard/square_64_P_32_4/): Hubbard/square_64_P_32_4, 5 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_32_4.json.
- [square 8x8, U = 6, n = 1](https://qmbl.org/i/Hubbard/square_64_P_32_6/): Hubbard/square_64_P_32_6, 1 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_32_6.json.
- [square 8x8, U = 8, n = 1](https://qmbl.org/i/Hubbard/square_64_P_32_8/): Hubbard/square_64_P_32_8, 4 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_P_32_8.json.
- [square 8x8, periodic/antiperiodic, U = 2, n = 1](https://qmbl.org/i/Hubbard/square_64_PA_32_2/): Hubbard/square_64_PA_32_2, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_PA_32_2.json.
- [square 8x8, periodic/antiperiodic, U = 4, n = 1](https://qmbl.org/i/Hubbard/square_64_PA_32_4/): Hubbard/square_64_PA_32_4, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_PA_32_4.json.
- [square 8x8, periodic/antiperiodic, U = 6, n = 1](https://qmbl.org/i/Hubbard/square_64_PA_32_6/): Hubbard/square_64_PA_32_6, 3 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_PA_32_6.json.
- [square 8x8, periodic/antiperiodic, U = 8, n = 1](https://qmbl.org/i/Hubbard/square_64_PA_32_8/): Hubbard/square_64_PA_32_8, 2 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_PA_32_8.json.
- [square 8x8, periodic/open, U = 8, n = 1](https://qmbl.org/i/Hubbard/square_64_PO_32_8/): Hubbard/square_64_PO_32_8, 3 energies, JSON at https://qmbl.org/api/i/Hubbard/square_64_PO_32_8.json.
- [SB-DMFT-MI-HF, size 9](https://qmbl.org/i/Impurity/SB-DMFT-MI-HF_9/): Impurity/SB-DMFT-MI-HF_9, 2 energies, JSON at https://qmbl.org/api/i/Impurity/SB-DMFT-MI-HF_9.json.
- [SB-DMFT-MT-AHF, size 9](https://qmbl.org/i/Impurity/SB-DMFT-MT-AHF_9/): Impurity/SB-DMFT-MT-AHF_9, 2 energies, JSON at https://qmbl.org/api/i/Impurity/SB-DMFT-MT-AHF_9.json.
- [SB-DMFT-MT-HF, size 9](https://qmbl.org/i/Impurity/SB-DMFT-MT-HF_9/): Impurity/SB-DMFT-MT-HF_9, 2 energies, JSON at https://qmbl.org/api/i/Impurity/SB-DMFT-MT-HF_9.json.
- [SB-IMP, size 9](https://qmbl.org/i/Impurity/SB-IMP_9/): Impurity/SB-IMP_9, 2 energies, JSON at https://qmbl.org/api/i/Impurity/SB-IMP_9.json.
- [TB-DMFT, size 119](https://qmbl.org/i/Impurity/TB-DMFT_119/): Impurity/TB-DMFT_119, 3 energies, JSON at https://qmbl.org/api/i/Impurity/TB-DMFT_119.json.
- [TB-DMFT, size 19](https://qmbl.org/i/Impurity/TB-DMFT_19/): Impurity/TB-DMFT_19, 3 energies, JSON at https://qmbl.org/api/i/Impurity/TB-DMFT_19.json.
- [TB-DMFT, size 309](https://qmbl.org/i/Impurity/TB-DMFT_309/): Impurity/TB-DMFT_309, 3 energies, JSON at https://qmbl.org/api/i/Impurity/TB-DMFT_309.json.
- [TB-DMFT, size 9](https://qmbl.org/i/Impurity/TB-DMFT_9/): Impurity/TB-DMFT_9, 3 energies, JSON at https://qmbl.org/api/i/Impurity/TB-DMFT_9.json.
- [TB-DMFT-SOC, size 119](https://qmbl.org/i/Impurity/TB-DMFT-SOC_119/): Impurity/TB-DMFT-SOC_119, 3 energies, JSON at https://qmbl.org/api/i/Impurity/TB-DMFT-SOC_119.json.
- [TB-DMFT-SOC, size 19](https://qmbl.org/i/Impurity/TB-DMFT-SOC_19/): Impurity/TB-DMFT-SOC_19, 3 energies, JSON at https://qmbl.org/api/i/Impurity/TB-DMFT-SOC_19.json.
- [TB-DMFT-SOC, size 309](https://qmbl.org/i/Impurity/TB-DMFT-SOC_309/): Impurity/TB-DMFT-SOC_309, 3 energies, JSON at https://qmbl.org/api/i/Impurity/TB-DMFT-SOC_309.json.
- [TB-DMFT-SOC, size 9](https://qmbl.org/i/Impurity/TB-DMFT-SOC_9/): Impurity/TB-DMFT-SOC_9, 3 energies, JSON at https://qmbl.org/api/i/Impurity/TB-DMFT-SOC_9.json.
- [rectangular 4x6, J2 = 0.5](https://qmbl.org/i/J1J2/rectangular-4x6_24_P_0.5/): J1J2/rectangular-4x6_24_P_0.5, 6 energies, JSON at https://qmbl.org/api/i/J1J2/rectangular-4x6_24_P_0.5.json.
- [square 10x10, J2 = 0.3](https://qmbl.org/i/J1J2/square_100_P_0.3/): J1J2/square_100_P_0.3, 4 energies, JSON at https://qmbl.org/api/i/J1J2/square_100_P_0.3.json.
- [square 10x10, J2 = 0.4](https://qmbl.org/i/J1J2/square_100_P_0.4/): J1J2/square_100_P_0.4, 5 energies, JSON at https://qmbl.org/api/i/J1J2/square_100_P_0.4.json.
- [square 10x10, J2 = 0.5](https://qmbl.org/i/J1J2/square_100_P_0.5/): J1J2/square_100_P_0.5, 15 energies, JSON at https://qmbl.org/api/i/J1J2/square_100_P_0.5.json.
- [square 10x10, J2 = 0.6](https://qmbl.org/i/J1J2/square_100_P_0.6/): J1J2/square_100_P_0.6, 5 energies, JSON at https://qmbl.org/api/i/J1J2/square_100_P_0.6.json.
- [square 10x10, J2 = 0.7](https://qmbl.org/i/J1J2/square_100_P_0.7/): J1J2/square_100_P_0.7, 4 energies, JSON at https://qmbl.org/api/i/J1J2/square_100_P_0.7.json.
- [square 10x10, J2 = 0.8](https://qmbl.org/i/J1J2/square_100_P_0.8/): J1J2/square_100_P_0.8, 5 energies, JSON at https://qmbl.org/api/i/J1J2/square_100_P_0.8.json.
- [square 10x10, J2 = 0.9](https://qmbl.org/i/J1J2/square_100_P_0.9/): J1J2/square_100_P_0.9, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_100_P_0.9.json.
- [square 10x10, J2 = 1](https://qmbl.org/i/J1J2/square_100_P_1/): J1J2/square_100_P_1, 5 energies, JSON at https://qmbl.org/api/i/J1J2/square_100_P_1.json.
- [square 4x4, J2 = 0.05](https://qmbl.org/i/J1J2/square_16_P_0.05/): J1J2/square_16_P_0.05, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.05.json.
- [square 4x4, J2 = 0.1](https://qmbl.org/i/J1J2/square_16_P_0.1/): J1J2/square_16_P_0.1, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.1.json.
- [square 4x4, J2 = 0.15](https://qmbl.org/i/J1J2/square_16_P_0.15/): J1J2/square_16_P_0.15, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.15.json.
- [square 4x4, J2 = 0.2](https://qmbl.org/i/J1J2/square_16_P_0.2/): J1J2/square_16_P_0.2, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.2.json.
- [square 4x4, J2 = 0.25](https://qmbl.org/i/J1J2/square_16_P_0.25/): J1J2/square_16_P_0.25, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.25.json.
- [square 4x4, J2 = 0.3](https://qmbl.org/i/J1J2/square_16_P_0.3/): J1J2/square_16_P_0.3, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.3.json.
- [square 4x4, J2 = 0.35](https://qmbl.org/i/J1J2/square_16_P_0.35/): J1J2/square_16_P_0.35, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.35.json.
- [square 4x4, J2 = 0.4](https://qmbl.org/i/J1J2/square_16_P_0.4/): J1J2/square_16_P_0.4, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.4.json.
- [square 4x4, J2 = 0.45](https://qmbl.org/i/J1J2/square_16_P_0.45/): J1J2/square_16_P_0.45, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.45.json.
- [square 4x4, J2 = 0.5](https://qmbl.org/i/J1J2/square_16_P_0.5/): J1J2/square_16_P_0.5, 6 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.5.json.
- [square 4x4, J2 = 0.6](https://qmbl.org/i/J1J2/square_16_P_0.6/): J1J2/square_16_P_0.6, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.6.json.
- [square 4x4, J2 = 0.65](https://qmbl.org/i/J1J2/square_16_P_0.65/): J1J2/square_16_P_0.65, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.65.json.
- [square 4x4, J2 = 0.7](https://qmbl.org/i/J1J2/square_16_P_0.7/): J1J2/square_16_P_0.7, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.7.json.
- [square 4x4, J2 = 0.75](https://qmbl.org/i/J1J2/square_16_P_0.75/): J1J2/square_16_P_0.75, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.75.json.
- [square 4x4, J2 = 0.8](https://qmbl.org/i/J1J2/square_16_P_0.8/): J1J2/square_16_P_0.8, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.8.json.
- [square 4x4, J2 = 0.85](https://qmbl.org/i/J1J2/square_16_P_0.85/): J1J2/square_16_P_0.85, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.85.json.
- [square 4x4, J2 = 0.9](https://qmbl.org/i/J1J2/square_16_P_0.9/): J1J2/square_16_P_0.9, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.9.json.
- [square 4x4, J2 = 0.95](https://qmbl.org/i/J1J2/square_16_P_0.95/): J1J2/square_16_P_0.95, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_0.95.json.
- [square 4x4, J2 = 1](https://qmbl.org/i/J1J2/square_16_P_1.0/): J1J2/square_16_P_1.0, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_16_P_1.0.json.
- [square 14x14, J2 = 0.5](https://qmbl.org/i/J1J2/square_196_P_0.5/): J1J2/square_196_P_0.5, 4 energies, JSON at https://qmbl.org/api/i/J1J2/square_196_P_0.5.json.
- [square 16x16, J2 = 0.5](https://qmbl.org/i/J1J2/square_256_P_0.5/): J1J2/square_256_P_0.5, 3 energies, JSON at https://qmbl.org/api/i/J1J2/square_256_P_0.5.json.
- [square 6x6, J2 = 0.3](https://qmbl.org/i/J1J2/square_36_P_0.3/): J1J2/square_36_P_0.3, 4 energies, JSON at https://qmbl.org/api/i/J1J2/square_36_P_0.3.json.
- [square 6x6, J2 = 0.4](https://qmbl.org/i/J1J2/square_36_P_0.4/): J1J2/square_36_P_0.4, 6 energies, JSON at https://qmbl.org/api/i/J1J2/square_36_P_0.4.json.
- [square 6x6, J2 = 0.5](https://qmbl.org/i/J1J2/square_36_P_0.5/): J1J2/square_36_P_0.5, 11 energies, JSON at https://qmbl.org/api/i/J1J2/square_36_P_0.5.json.
- [square 6x6, J2 = 0.6](https://qmbl.org/i/J1J2/square_36_P_0.6/): J1J2/square_36_P_0.6, 8 energies, JSON at https://qmbl.org/api/i/J1J2/square_36_P_0.6.json.
- [square 6x6, J2 = 0.7](https://qmbl.org/i/J1J2/square_36_P_0.7/): J1J2/square_36_P_0.7, 5 energies, JSON at https://qmbl.org/api/i/J1J2/square_36_P_0.7.json.
- [square 6x6, J2 = 0.8](https://qmbl.org/i/J1J2/square_36_P_0.8/): J1J2/square_36_P_0.8, 6 energies, JSON at https://qmbl.org/api/i/J1J2/square_36_P_0.8.json.
- [square 6x6, J2 = 0.9](https://qmbl.org/i/J1J2/square_36_P_0.9/): J1J2/square_36_P_0.9, 4 energies, JSON at https://qmbl.org/api/i/J1J2/square_36_P_0.9.json.
- [square 6x6, J2 = 1](https://qmbl.org/i/J1J2/square_36_P_1/): J1J2/square_36_P_1, 6 energies, JSON at https://qmbl.org/api/i/J1J2/square_36_P_1.json.
- [square, 40 sites, J2 = 0.1](https://qmbl.org/i/J1J2/square_40_P_0.1/): J1J2/square_40_P_0.1, 1 energies, JSON at https://qmbl.org/api/i/J1J2/square_40_P_0.1.json.
- [square, 40 sites, J2 = 0.2](https://qmbl.org/i/J1J2/square_40_P_0.2/): J1J2/square_40_P_0.2, 1 energies, JSON at https://qmbl.org/api/i/J1J2/square_40_P_0.2.json.
- [square, 40 sites, J2 = 0.3](https://qmbl.org/i/J1J2/square_40_P_0.3/): J1J2/square_40_P_0.3, 1 energies, JSON at https://qmbl.org/api/i/J1J2/square_40_P_0.3.json.
- [square, 40 sites, J2 = 0.4](https://qmbl.org/i/J1J2/square_40_P_0.4/): J1J2/square_40_P_0.4, 1 energies, JSON at https://qmbl.org/api/i/J1J2/square_40_P_0.4.json.
- [square, 40 sites, J2 = 0.5](https://qmbl.org/i/J1J2/square_40_P_0.5/): J1J2/square_40_P_0.5, 1 energies, JSON at https://qmbl.org/api/i/J1J2/square_40_P_0.5.json.
- [square, 40 sites, J2 = 0.55](https://qmbl.org/i/J1J2/square_40_P_0.55/): J1J2/square_40_P_0.55, 1 energies, JSON at https://qmbl.org/api/i/J1J2/square_40_P_0.55.json.
- [square, 40 sites, J2 = 0.6](https://qmbl.org/i/J1J2/square_40_P_0.6/): J1J2/square_40_P_0.6, 1 energies, JSON at https://qmbl.org/api/i/J1J2/square_40_P_0.6.json.
- [square, 40 sites, J2 = 0.65](https://qmbl.org/i/J1J2/square_40_P_0.65/): J1J2/square_40_P_0.65, 1 energies, JSON at https://qmbl.org/api/i/J1J2/square_40_P_0.65.json.
- [square, 40 sites, J2 = 0.7](https://qmbl.org/i/J1J2/square_40_P_0.7/): J1J2/square_40_P_0.7, 1 energies, JSON at https://qmbl.org/api/i/J1J2/square_40_P_0.7.json.
- [square, 40 sites, J2 = 0.8](https://qmbl.org/i/J1J2/square_40_P_0.8/): J1J2/square_40_P_0.8, 1 energies, JSON at https://qmbl.org/api/i/J1J2/square_40_P_0.8.json.
- [square, 40 sites, J2 = 0.9](https://qmbl.org/i/J1J2/square_40_P_0.9/): J1J2/square_40_P_0.9, 1 energies, JSON at https://qmbl.org/api/i/J1J2/square_40_P_0.9.json.
- [square, 40 sites, J2 = 1](https://qmbl.org/i/J1J2/square_40_P_1/): J1J2/square_40_P_1, 1 energies, JSON at https://qmbl.org/api/i/J1J2/square_40_P_1.json.
- [square 20x20, J2 = 0.5](https://qmbl.org/i/J1J2/square_400_P_0.5/): J1J2/square_400_P_0.5, 2 energies, JSON at https://qmbl.org/api/i/J1J2/square_400_P_0.5.json.
- [square 8x8, J2 = 0.5](https://qmbl.org/i/J1J2/square_64_P_0.5/): J1J2/square_64_P_0.5, 8 energies, JSON at https://qmbl.org/api/i/J1J2/square_64_P_0.5.json.
- [square 8x8, J2 = 0.55](https://qmbl.org/i/J1J2/square_64_P_0.55/): J1J2/square_64_P_0.55, 1 energies, JSON at https://qmbl.org/api/i/J1J2/square_64_P_0.55.json.
- [triangular, 108 sites, J2 = 0.125](https://qmbl.org/i/J1J2/triangular_108_P_0.125/): J1J2/triangular_108_P_0.125, 4 energies, JSON at https://qmbl.org/api/i/J1J2/triangular_108_P_0.125.json.
- [triangular 12x12, J2 = 0.125](https://qmbl.org/i/J1J2/triangular_144_P_0.125/): J1J2/triangular_144_P_0.125, 4 energies, JSON at https://qmbl.org/api/i/J1J2/triangular_144_P_0.125.json.
- [triangular, 48 sites, J2 = 0.125](https://qmbl.org/i/J1J2/triangular_48_P_0.125/): J1J2/triangular_48_P_0.125, 48 energies, JSON at https://qmbl.org/api/i/J1J2/triangular_48_P_0.125.json.
- [chain, 10 sites, open, h = 1](https://qmbl.org/i/TFIsing/chain_10_O_1/): TFIsing/chain_10_O_1, 6 energies, JSON at https://qmbl.org/api/i/TFIsing/chain_10_O_1.json.
- [chain, 10 sites, h = 1](https://qmbl.org/i/TFIsing/chain_10_P_1/): TFIsing/chain_10_P_1, 4 energies, JSON at https://qmbl.org/api/i/TFIsing/chain_10_P_1.json.
- [chain, 32 sites, h = 0.5](https://qmbl.org/i/TFIsing/chain_32_P_0.5/): TFIsing/chain_32_P_0.5, 5 energies, JSON at https://qmbl.org/api/i/TFIsing/chain_32_P_0.5.json.
- [chain, 32 sites, h = 1](https://qmbl.org/i/TFIsing/chain_32_P_1/): TFIsing/chain_32_P_1, 5 energies, JSON at https://qmbl.org/api/i/TFIsing/chain_32_P_1.json.
- [square 12x12, open, h = 3](https://qmbl.org/i/TFIsing/square_144_O_3/): TFIsing/square_144_O_3, 4 energies, JSON at https://qmbl.org/api/i/TFIsing/square_144_O_3.json.
- [square 6x6, h = 3](https://qmbl.org/i/TFIsing/square_36_P_3/): TFIsing/square_36_P_3, 4 energies, JSON at https://qmbl.org/api/i/TFIsing/square_36_P_3.json.
- [square 20x20, open, h = 3](https://qmbl.org/i/TFIsing/square_400_O_3/): TFIsing/square_400_O_3, 7 energies, JSON at https://qmbl.org/api/i/TFIsing/square_400_O_3.json.
- [chain, 32 sites, V = 1, n = 0.5](https://qmbl.org/i/tV/chain_32_P_16_1/): tV/chain_32_P_16_1, 4 energies, JSON at https://qmbl.org/api/i/tV/chain_32_P_16_1.json.
- [chain, 32 sites, V = 2, n = 0.5](https://qmbl.org/i/tV/chain_32_P_16_2/): tV/chain_32_P_16_2, 3 energies, JSON at https://qmbl.org/api/i/tV/chain_32_P_16_2.json.
- [chain, 32 sites, V = 4, n = 0.5](https://qmbl.org/i/tV/chain_32_P_16_4/): tV/chain_32_P_16_4, 3 energies, JSON at https://qmbl.org/api/i/tV/chain_32_P_16_4.json.
- [square 4x4, V = 0.01, n = 0.3125](https://qmbl.org/i/tV/square_16_P_5_0.01/): tV/square_16_P_5_0.01, 3 energies, JSON at https://qmbl.org/api/i/tV/square_16_P_5_0.01.json.
- [square 4x4, V = 0.1, n = 0.3125](https://qmbl.org/i/tV/square_16_P_5_0.1/): tV/square_16_P_5_0.1, 5 energies, JSON at https://qmbl.org/api/i/tV/square_16_P_5_0.1.json.
- [square 4x4, V = 1, n = 0.3125](https://qmbl.org/i/tV/square_16_P_5_1/): tV/square_16_P_5_1, 5 energies, JSON at https://qmbl.org/api/i/tV/square_16_P_5_1.json.
- [square 4x4, V = 10, n = 0.3125](https://qmbl.org/i/tV/square_16_P_5_10/): tV/square_16_P_5_10, 5 energies, JSON at https://qmbl.org/api/i/tV/square_16_P_5_10.json.
- [square 6x6, V = 0.01, n ≈ 0.3611](https://qmbl.org/i/tV/square_36_P_13_0.01/): tV/square_36_P_13_0.01, 3 energies, JSON at https://qmbl.org/api/i/tV/square_36_P_13_0.01.json.
- [square 6x6, V = 0.1, n ≈ 0.3611](https://qmbl.org/i/tV/square_36_P_13_0.1/): tV/square_36_P_13_0.1, 4 energies, JSON at https://qmbl.org/api/i/tV/square_36_P_13_0.1.json.
- [square 6x6, V = 1, n ≈ 0.3611](https://qmbl.org/i/tV/square_36_P_13_1/): tV/square_36_P_13_1, 4 energies, JSON at https://qmbl.org/api/i/tV/square_36_P_13_1.json.
- [square 6x6, V = 10, n ≈ 0.3611](https://qmbl.org/i/tV/square_36_P_13_10/): tV/square_36_P_13_10, 4 energies, JSON at https://qmbl.org/api/i/tV/square_36_P_13_10.json.
- [square 8x8, V = 1, n = 0.5](https://qmbl.org/i/tV/square_64_P_32_1/): tV/square_64_P_32_1, 2 energies, JSON at https://qmbl.org/api/i/tV/square_64_P_32_1.json.
- [square 8x8, V = 2, n = 0.5](https://qmbl.org/i/tV/square_64_P_32_2/): tV/square_64_P_32_2, 2 energies, JSON at https://qmbl.org/api/i/tV/square_64_P_32_2.json.
- [square 8x8, V = 4, n = 0.5](https://qmbl.org/i/tV/square_64_P_32_4/): tV/square_64_P_32_4, 2 energies, JSON at https://qmbl.org/api/i/tV/square_64_P_32_4.json.