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All instances / Heisenberg

Heisenberg pyrochlore 2x2x6 (96 sites)

Record

-0.4917(4) E/N (S.S)

mVMC

Astrakhantsev et al. (2021) · lowest unflagged energy published, a strict variational bound (rules §6)

The Hamiltonian

H = ∑⟨ij⟩ σi·σj

Nearest-neighbour Heisenberg antiferromagnet, J = 1, written with Pauli matrices.

lattice
pyrochlore-2x2x6
sites
96
boundary
periodic
energies
2

Stored as a total energy; 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. On a solved instance the exact energy is the record; otherwise the lowest unflagged energy of any group holds it (rules §6).

Strict variational upper bounds (2)

Energies that a variational state reached (VMC, DMRG and MPS at finite bond dimension, PEPS, NQS, VQE). Each is an upper bound on the ground-state energy.

E/N (S.S)distance to recordσVar(E)V-score methodsourceyear
-0.4917record 0 4.0e-4 n/a n/a mVMC
peer reviewed
Astrakhantsev et al. (2021) 2021
-0.490 1.7e-3 1.0e-3 n/a n/a CNN
peer reviewed
Astrakhantsev et al. (2021) 2021

How these numbers were read

Where each number below was read, and how it was checked.

-0.4917(4), mVMC

Checked 2026-10-22 · source text of arXiv:2101.08787 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading

Reported as. -0.4917(4)

Appendix H Table II, geometry 4x2^2x6, column mVMC, first line of cell; sources/2101.08787.txt line 1130; version read: arXiv text, Appendix H Table II (sources/2101.08787.txt) | Spin-1/2 operators S = sigma/2, J = 1; Table II caption: first line of each cell is the energy per site (S.S units). Cluster 4 x L^3 is L^3 FCC primitive cells of 4 sites (4 x 2^3 = VarBench's pyrochlore-2x2x2_32_P).

-0.490(1), CNN

Checked 2026-10-22 · source text of arXiv:2101.08787 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading

Reported as. -0.490(1)

Appendix H Table II, geometry 4x2^2x6, column NQS CNN, first line of cell; sources/2101.08787.txt line 1130; version read: arXiv text, Appendix H Table II (sources/2101.08787.txt) | Spin-1/2 operators S = sigma/2, J = 1; Table II caption: first line of each cell is the energy per site (S.S units). Cluster 4 x L^3 is L^3 FCC primitive cells of 4 sites (4 x 2^3 = VarBench's pyrochlore-2x2x2_32_P).

Coverage

Newest published number here: 2021.

This instance as data

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