Stability of thermal equilibrium in long-range quantum systems

TL;DR

This paper demonstrates that in long-range quantum systems, the stability of thermal equilibrium and local measurements is guaranteed at high temperatures due to correlation decay and Lieb-Robinson bounds, supporting the robustness of analog quantum simulations.

Contribution

It analytically and numerically establishes the stability of local observables in long-range quantum systems at high temperatures, linking it to correlation decay and Lieb-Robinson bounds.

Findings

Stability of local expectation values follows from correlation decay and Lieb-Robinson bounds.

Stability holds at high temperature regimes.

Numerical evidence suggests extended stability in long-range systems.

Abstract

Experimental realizations of spin models are irremediably prone to errors, which can propagate through the system corrupting experimental signals. We study how such errors affect the measurement of local observables in systems with long-range interactions, where perturbations can spread more rapidly. Specifically, we focus on the stability of thermal equilibrium and investigate its relation to the correlation structure of the system, both analytically and numerically. As a main result, we prove that the stability of local expectation values follows from the decay of correlations on the Gibbs state and the Lieb-Robinson bound, and hence that stability always holds at high temperature. We also provide numerical evidence that this stability extends to an even larger regime of interacting long-range systems. Our results support the robustness of analog simulation platforms for long-range models, and provide further evidence that computing physical quantities of interest can be significantly easier than performing arbitrary quantum computations.