Related papers: Convex-Gaussianity of fermionic Gibbs states in perturbation theory

Convex-Gaussianity of fermionic Gibbs states in perturbation theory

URL: http://arxiv.org/abs/2609.09608v1
Date: Wed, 09 Sep 2026 02:03:21 GMT
Title: Convex-Gaussianity of fermionic Gibbs states in perturbation theory
Abstract summary: We study the structure of Gibbs states in weakly interacting fermionic systems.<n>We show that the Gibbs state remains convex-Gaussian up to $le Obig(vertUvert-1log(vertUvert/(Dverttvert)big)$, revealing a mechanism for convex-Gaussianity.
Score: 1.4323566945483497
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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 $β\le O(\log(1/ε))$. Moreover, we prove that this bound is asymptotically tight by establishing that $β\le Θ(\log(1/ε))$ is necessary for certain sparse Hamiltonians. This general framework applies directly to the weak-coupling (small-$\vert{}U\vert{}$) 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-$\vert{}t\vert{}$) regime, we show that the Gibbs state remains convex-Gaussian up to $β\le O\big(\vert{}U\vert{}^{-1}\log(\vert{}U\vert{}/(D\vert{}t\vert{}))\big)$, revealing a mechanism for convex-Gaussianity distinct from the weak-coupling setting.

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