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All instances / J1-J2

J1-J2 triangular 12x12, J2 = 0.125

J1J2/triangular_144_P_0.125

Record

-0.51218(9) E/N (S.S)

GCNN + Lanczos step

Roth et al. (2022) · lowest eligible strict variational bound (rules §6)

The Hamiltonian

H = ∑⟨ij⟩ σi·σj + J2⟨⟨ij⟩⟩ σi·σj

J1 = 1, J2 = 0.125, nearest and next-nearest neighbours, written with Pauli matrices.

lattice
triangular
sites
144
boundary
periodic
J2
0.125
energies
4

Stored as a total energy in the convention of VarBench; quoted here as E/N (S.S), which is what the papers report (how the conversion works).

Every published energy

Grouped by what the number is. Ranking happens only inside the first group.

Strict variational upper bounds (3)

The record is the lowest eligible energy in this group, and only this group.

E/N (S.S)σVar(E)V-score methodsourceyear
-0.51218(9)record 9.0e-5 n/a n/a GCNN + Lanczos step
peer reviewed
Roth et al. (2022) 2022
-0.51101(6) 6.0e-5 n/a n/a GCNN (deep group-equivariant CNN)
peer reviewed
Roth et al. (2022) 2022
-0.510558(5) 5.0e-6 n/a n/a Gutzwiller-projected fermionic state + Lanczos step
quoted from another paper
Iqbal, Hu, Thomale, Poilblanc & n/a

Extrapolations (1)

Zero-variance, bond-dimension or Trotter-error extrapolations. Not a bound: no ansatz ever reached the number, so it cannot hold the record.

E/N (S.S)σVar(E)V-score methodsourceyear
-0.5127500 n/a n/a n/a Thermodynamic-limit estimate interpolated to this size (1/L^3)
quoted from another paper
Iqbal, Hu, Thomale, Poilblanc & n/a

How these numbers were read

Rows added after the VarBench import record where the number came from.

-0.5127500 ○ — Thermodynamic-limit estimate interpolated to this size...

Checked 2026-09-14 · arXiv PDF extracted locally with pypdf in layout mode, no LLM transcription

Reported as. -0.51275 per site in S.S units

Read from Table III of arXiv:2211.07749 (J1-J2 triangular lattice, periodic, energies in units of J1 per spin, i.e. the S.S per-site convention), extracted from the PDF with pypdf in layout mode so the column positions are unambiguous. Column "Exact/Interpolated [10,63]". Per the caption this is NOT an exact energy above 36 sites: it is built from the thermodynamic-limit estimate of Ref. [10] and the exact 36-site energy, assuming finite-size effects scale as 1/L^3. Carried as `extrapolated` (RULES.md 4).

-0.51218(9) — GCNN + Lanczos step

Checked 2026-09-14 · arXiv PDF extracted locally with pypdf in layout mode, no LLM transcription

Reported as. -0.51218 (+/- 0.00009) per site in S.S units

Read from Table III of arXiv:2211.07749 (J1-J2 triangular lattice, periodic, energies in units of J1 per spin, i.e. the S.S per-site convention), extracted from the PDF with pypdf in layout mode so the column positions are unambiguous. Column "GCNN+LS" at J2/J1 = 1/8, N = 144.

-0.51101(6) — GCNN (deep group-equivariant CNN)

Checked 2026-09-14 · arXiv PDF extracted locally with pypdf in layout mode, no LLM transcription

Reported as. -0.51101 (+/- 0.00006) per site in S.S units

Read from Table III of arXiv:2211.07749 (J1-J2 triangular lattice, periodic, energies in units of J1 per spin, i.e. the S.S per-site convention), extracted from the PDF with pypdf in layout mode so the column positions are unambiguous. Row J2/J1 = 1/8, N = 144.

-0.510558(5) — Gutzwiller-projected fermionic state + Lanczos step

Checked 2026-09-14 · arXiv PDF extracted locally with pypdf in layout mode, no LLM transcription

Reported as. -0.510558 (+/- 0.000005) per site in S.S units

Read from Table III of arXiv:2211.07749 (J1-J2 triangular lattice, periodic, energies in units of J1 per spin, i.e. the S.S per-site convention), extracted from the PDF with pypdf in layout mode so the column positions are unambiguous. Column "Gutzwiller+LS [10]" = Phys. Rev. B 93, 144411 (2016).

Coverage

Newest published number here: 2022. 4 rows added from the 2026-09 literature sweep, on top of the VarBench snapshot of 2024-10-22.

This instance as data

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