QMBLthe quantum many-body leaderboard

All instances / Hubbard

Hubbard rectangular 8x24, U = 8, n = 0.875

Best values (rules §6)

best variational -0.7546 VMC (tensor BF)
Liang (2025) · the lowest unflagged variational energy, a strict variational bound

Energies as E/site. Classes are different claims and are not ranked against each other.

The Hamiltonian

H = −t ∑⟨ij⟩,σ (c†iσcjσ + h.c.) + U ∑i ni↑ni↓

t = 1, U = 8, N↑ = N↓ = 84 on 192 sites.

lattice
rectangular-8x24
sites
192
boundary
periodic
Nf
84
U
8
energies
2

Stored as a total energy; quoted here as E/site, 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 (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/sitedistance to class bestσVar(E)V-score methodsourcecodeyearcomment
-0.7546best variational 0 n/a n/a n/a VMC (tensor BF)
peer reviewed
 Liang (2025) 2025
-0.75 4.6e-3 n/a n/a n/a VMC (tensor BF)
peer reviewed
 Liang (2025) 2025

How these numbers were read

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

-0.7546, VMC (tensor BF)

Checked 2026-09-15 · source text of arXiv:2507.01856 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table

Reported as. -0.7546

Table V of arXiv:2507.01856 (pypdf layout text, line 400), 8x24, t' = 0, NN backflow, column Ep = 1 | n = 0.875, U = 8 (Table V caption); PBC: the 8x16 Ep = 1 value equals Table II's 8x16 PBC row, and Figs. 4 and 8 state the 8x32 lattice is under PBC

-0.75, VMC (tensor BF)

Checked 2026-09-15 · source text of arXiv:2507.01856 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table

Reported as. -0.7500

Table V of arXiv:2507.01856 (pypdf layout text, line 400), 8x24, t' = 0, NN backflow, column Ep = 0 | n = 0.875, U = 8 (Table V caption); PBC: the 8x16 Ep = 1 value equals Table II's 8x16 PBC row, and Figs. 4 and 8 state the 8x32 lattice is under PBC

Coverage

Newest published number here: 2025.

This instance as data

JSON · source file on GitHub · add a result · open an issue about this instance