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All instances / Heisenberg

Heisenberg pyrochlore 3x3x3 (108 sites)

Best values (rules §6)

best variational -0.4871(1) VMC (PP)
Astrakhantsev et al. (2021) · the lowest unflagged variational energy, a strict variational bound

Energies as E/N (S.S). Classes are different claims and are not ranked against each other.

The Hamiltonian

H = ∑⟨ij⟩ σi·σj

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

lattice
pyrochlore-3x3x3
sites
108
boundary
periodic
energies
3

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. The exact energy comes first where there is one; in every other group the lowest unflagged energy is its best value, and each row's distance is to that best (rules §6).

Strict variational upper bounds (3)

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 class bestσVar(E)V-score methodsourcecodeyearcomment
-0.4871best variational 0 1.0e-4 3.99e+1 9.7e-2 VMC (PP) Astrakhantsev et al. (2021) uses mVMC 2021
-0.4851 2.0e-3 n/a n/a n/a DMRG
quoted from another paper peer reviewed
Hagymási et al. (2020) 2020
-0.4826 4.5e-3 2.0e-4 1.81e+1 4.5e-2 VMC (CNN) Astrakhantsev et al. (2021) uses NetKet 2021

How these numbers were read

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

-0.4871(1), VMC (PP)

Checked 2026-10-15 · published PDF Phys. Rev. X 11, 041021 (2021) (open access), sources/journal/prx11-041021.pdf, sha256 e65c26b3, pypdf layout (ð1Þ = (1) in the font); arXiv:2101.08787v2 compared (qmbl/sources/2101.08787.txt Table II identical)

Reported as. -0.4871(1) per site (S.S, J = 1)

H = j1 sum h_lambda(i,j) + j2 sum ..., h_lambda = lambda/2 (S+S- + S-S+) + SzSz (Eqs. 1-2), Heisenberg point lambda = 1, j2 = 0; Table II: 'The ground-state energy per site is listed in the first line of every cell'; 'We consider pyrochlore clusters with periodic boundary conditions'. Geometry 4 x L^3 = 4L^3 sites. Stored Pauli total = 4 x N x E/N. Own computation (mVMC / NQS CNN columns). The paper prints no energy variance: the stored energy_variance is the VarBench upload's only. Published 29 October 2021, peer reviewed. Lies below the DMRG column -0.4851 [38] of the same row; lowest stored energy on the instance (record). Journal = arXiv v2. No duplicate.

-0.4826(2), VMC (CNN)

Checked 2026-10-15 · published PDF Phys. Rev. X 11, 041021 (2021) (open access), sources/journal/prx11-041021.pdf, sha256 e65c26b3, pypdf layout (ð1Þ = (1) in the font); arXiv:2101.08787v2 compared (qmbl/sources/2101.08787.txt Table II identical)

Reported as. -0.4826(2) per site (S.S, J = 1)

H = j1 sum h_lambda(i,j) + j2 sum ..., h_lambda = lambda/2 (S+S- + S-S+) + SzSz (Eqs. 1-2), Heisenberg point lambda = 1, j2 = 0; Table II: 'The ground-state energy per site is listed in the first line of every cell'; 'We consider pyrochlore clusters with periodic boundary conditions'. Geometry 4 x L^3 = 4L^3 sites. Stored Pauli total = 4 x N x E/N. Own computation (mVMC / NQS CNN columns). The paper prints no energy variance: the stored energy_variance is the VarBench upload's only. Published 29 October 2021, peer reviewed. No duplicate.

Coverage

Newest published number here: 2021.

This instance as data

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