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arXiv · 2505.09730

High-Temperature Fermionic Gibbs States are Mixtures of Gaussian States

Akshar Ramkumar·Yiyi Cai·Yu Tong·Jiaqing Jiang
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Abstract

Efficient simulation of a quantum system generally relies on structural properties of the quantum state. Motivated by the recent results by Bakshi et al. on the sudden death of entanglement in high-temperature Gibbs states of quantum spin systems, we study the high-temperature Gibbs states of bounded-degree local fermionic Hamiltonians, which include the special case of geometrically local fermionic systems. We prove that at a sufficiently high temperature that is independent of the system size, the Gibbs state is a probabilistic mixture of fermionic Gaussian states. This forms the basis of an efficient classical algorithm to prepare the Gibbs state by sampling from a distribution of fermionic Gaussian states. As a contrasting example, we show that high-temperature Gibbs states of the Sachdev-Ye-Kitaev (SYK) model are not convex mixtures of Gaussian states.

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Akshar Ramkumar, Yiyi Cai, Yu Tong, Jiaqing Jiang. 2025-05-14. High-Temperature Fermionic Gibbs States are Mixtures of Gaussian States. https://arxiv.org/abs/2505.09730

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