QMBL: the Quantum Many-Body Leaderboard. A live record of published ground-state energies for lattice Hamiltonians and the electron gas
cond-mat.str-el, quant-ph
Submitted: 2026-10-12
Updated: 2026-10-20
Comments: 2 pages, 2 figures. Data: https://doi.org/10.5281/zenodo.23239245; leaderboard: https://qmbl.org
Code: https://github.com/quantum-many-body-leaderboard/quantum-many-body-leaderboard
Project page: https://www.qmbl.org
License: http://creativecommons.org/licenses/by/4.0/
The gist: In condensed matter physics, scientists explore phase diagrams of matter through various methods (analysis, numerics, experiment) and achieve consensus when enough methods agree.
Abstract
In condensed matter physics, scientists explore phase diagrams of matter through various methods (analysis, numerics, experiment) and achieve consensus when enough methods agree. The quality of variational results for quantum many-body ground states is mainly judged by energy values and respective errors. Here, we present QMBL, the Quantum Many-Body Leaderboard (https://www.qmbl.org), serving as the energy layer of the scientific consensus. It is a maintained, interactive record of published ground-state energies for lattice Hamiltonians. The latest release v0.4.0 holds 1434 energies on 395 instances of six model families and collects all of the community's efforts into one view. Of those instances 153 have no exact solution and any new record serves as a direct improvement to an open science problem. They are the targets of a companion benchmark, QMBL: Open Problems.
Sources
- Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
- Variational Benchmarks for Quantum Many-Body Problems
- OptiMat Alloys: a FAIR, living database of multi-principal element alloys enabled by a conversational agent
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