High-Temperature Fermionic Gibbs States are Mixtures of Gaussian States

TL;DR

This paper proves that high-temperature Gibbs states of bounded-degree local fermionic Hamiltonians can be efficiently approximated as mixtures of Gaussian states, enabling classical simulation, unlike certain models like the SYK model.

Contribution

It establishes that high-temperature Gibbs states of bounded-degree local fermionic Hamiltonians are mixtures of Gaussian states, facilitating efficient classical simulation.

Findings

High-temperature Gibbs states are mixtures of Gaussian states for bounded-degree fermionic systems.

Such states can be prepared efficiently via classical sampling algorithms.

High-temperature Gibbs states of the SYK model are not Gaussian mixtures.

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.