Heisenberg pyrochlore 4x4x4 (256 sites)

Heisenberg/pyrochlore-4x4x4_256_P

Record

-0.48310(7) E/N (S.S)

mVMC with SU(2) and symmetry projections

Astrakhantsev et al. (2021) · lowest eligible strict variational bound (rules §6)

The Hamiltonian

H = ∑_⟨ij⟩ σ_i·σ_j

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

lattice: pyrochlore-4x4x4
sites: 256
boundary: periodic
energies: 2

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 (2)

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

E/N (S.S)	σ	Var(E)	V-score	method	source	year
-0.4855000 ○	n/a	n/a	n/a	Generalized RVB ansatz, unrestricted VMC optimization (no quantum-number projection) preprint ineligible: sampled, no error bar	Closely competing valence bond c	n/a
-0.48310(7)record	7.4e-5	1.09e+2	1.1e-1	mVMC with SU(2) and symmetry projections	Astrakhantsev et al. (2021)	2021

How these numbers were read

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

-0.4855000 ○ — Generalized RVB ansatz, unrestricted VMC optimization (no...

Checked 2026-09-15 · arXiv PDF text extracted locally with pypdf in layout mode, no LLM transcription

Reported as. E0 ~ -0.4855 J/site, approximate, no error bar

Sec. A: "The obtained ground state energy is E0 ~ -0.5118 J/site for the L = 2 cluster and E0 ~ -0.4855 J/site for the L = 4 cluster", periodic boundary conditions on both; the L = 4 cluster carries Nv = 4N^2 = 262144 parameters, so N = 256. Units: the same passage quotes the mVMC energy -0.5162 J/site for L = 2, which is the pyrochlore-2x2x2_32_P record -0.516266 in the S.S per-site convention. Approximate and without an error bar, so it is eligible for nothing (RULES.md 6). It is nonetheless 0.5% below the VarBench mVMC record -0.4830957, although the ansatz has no symmetry projection and sits above mVMC at L = 2 - which says more about that record than about this row.

Coverage

Newest published number here: 2021. 1 row added from the 2026-09 literature sweep, on top of the VarBench snapshot of 2024-10-22.

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