Convex-Gaussianity of fermionic Gibbs states in perturbation theory
Abstract
We study the structure of Gibbs states in weakly perturbed interacting fermionic systems. First, for a sparse Hamiltonian H=H0+V with a quadratic term H0 and a non-quadratic perturbation V of scale ε, we show that the Gibbs state ρβ decomposes into a convex combination of Gaussian states whenever the inverse temperature satisfies β≤ O(log(1/ε)). Moreover, we prove that this bound is asymptotically tight by establishing that β≤ Θ(log(1/ε)) is necessary for certain sparse Hamiltonians. This general framework applies directly to the weak-coupling (small-|U|) regime of the Fermi--Hubbard model with hopping t and on-site interaction U on any graph of maximum degree D. Complementarily, in the strong-coupling (small-|t|) regime, we show that the Gibbs state remains convex-Gaussian up to β≤ O(|U|−1log(|U|/(D|t|))), revealing a mechanism for convex-Gaussianity distinct from the weak-coupling setting.
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BibTeX
@misc{bu2026convexgaussianity,
title = {{Convex-Gaussianity of fermionic Gibbs states in perturbation theory}},
author = {Kaifeng Bu and Yuanjie Ren},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09608},
eprint = {2609.09608},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09608},
}
RIS
TY - UNPB
TI - Convex-Gaussianity of fermionic Gibbs states in perturbation theory
AU - Kaifeng Bu
AU - Yuanjie Ren
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09608
UR - https://arxiv.org/abs/2609.09608
AB - We study the structure of Gibbs states in weakly perturbed interacting fermionic systems. First, for a sparse Hamiltonian H=H_0+V with a quadratic term H_0 and a non-quadratic perturbation V of scale ε, we show that the Gibbs state ρ_β decomposes into a convex combination of Gaussian states whenever the inverse temperature satisfies β≤ O(log(1/ε)). Moreover, we prove that this bound is asymptotically tight by establishing that β≤ Θ(log(1/ε)) is necessary for certain sparse Hamiltonians. This general framework applies directly to the weak-coupling (small-|U|) regime of the Fermi--Hubbard model with hopping t and on-site interaction U on any graph of maximum degree D. Complementarily, in the strong-coupling (small-|t|) regime, we show that the Gibbs state remains convex-Gaussian up to β≤ O(|U|^−1log(|U|/(D|t|))), revealing a mechanism for convex-Gaussianity distinct from the weak-coupling setting.
ER -