Weakly interacting fermionic Gibbs states are Gaussian mixtures and classically simulable
Abstract
Identifying regimes in which interacting fermionic systems admit efficient classical simulation is a crucial task in quantum many-body physics. In this work, we rigorously establish the Gaussianity and classical simulability of sufficiently weakly interacting fermions. For the Gibbs state of a local interacting fermionic Hamiltonian H=H0+V at any finite temperature and in any spatial dimension, where H0 is quadratic and V is the interaction term, we show that there exists a positive interaction strength below which the Gibbs state is a convex mixture of fermionic Gaussian states. Moreover, based on this structure, we construct a polynomial-time classical sampler for the Gibbs state via Metropolis updates on a tree whose leaves are Gaussian states.
Related
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BibTeX
@misc{han2026weakly,
title = {{Weakly interacting fermionic Gibbs states are Gaussian mixtures and classically simulable}},
author = {Zhengyi Han and Yuanchen Zhao and Zi-Wen Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35159},
eprint = {2609.35159},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35159},
}
RIS
TY - UNPB
TI - Weakly interacting fermionic Gibbs states are Gaussian mixtures and classically simulable
AU - Zhengyi Han
AU - Yuanchen Zhao
AU - Zi-Wen Liu
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35159
UR - https://arxiv.org/abs/2609.35159
AB - Identifying regimes in which interacting fermionic systems admit efficient classical simulation is a crucial task in quantum many-body physics. In this work, we rigorously establish the Gaussianity and classical simulability of sufficiently weakly interacting fermions. For the Gibbs state of a local interacting fermionic Hamiltonian H=H_0+V at any finite temperature and in any spatial dimension, where H_0 is quadratic and V is the interaction term, we show that there exists a positive interaction strength below which the Gibbs state is a convex mixture of fermionic Gaussian states. Moreover, based on this structure, we construct a polynomial-time classical sampler for the Gibbs state via Metropolis updates on a tree whose leaves are Gaussian states.
ER -