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arXiv · 2609.35159

Weakly interacting fermionic Gibbs states are Gaussian mixtures and classically simulable

Zhengyi Han·Yuanchen Zhao·Zi-Wen Liu
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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 $H=H_0+V$ 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.

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Zhengyi Han, Yuanchen Zhao, Zi-Wen Liu. 2026-09-28. Weakly interacting fermionic Gibbs states are Gaussian mixtures and classically simulable. https://arxiv.org/abs/2609.35159

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