Universal nature of replica symmetry breaking in quantum systems with Gaussian disorder

TL;DR

This paper investigates quantum spin systems with Gaussian disorder, demonstrating the universal vanishing of variance in physical quantities and exploring the conditions under which replica symmetry breaking occurs.

Contribution

It establishes the universal vanishing of variance for physical quantities and links finite variance to spontaneous replica symmetry breaking in quantum systems.

Findings

Variance of physical quantities vanishes in the infinite volume limit.

Finite variance of the overlap operator implies spontaneous replica symmetry breaking.

Replica symmetry breaking phenomena are characterized in different Gibbs states.

Abstract

We study quantum spin systems with quenched Gaussian disorder. We prove that the variance of all physical quantities in a certain class vanishes in the infinite volume limit. We study also replica symmetry breaking phenomena, where the variance of an overlap operator in the other class does not vanish in the replica symmetric Gibbs state. On the other hand, it vanishes in a spontaneous replica symmetry breaking Gibbs state defined by applying an infinitesimal replica symmetry breaking field. We prove also that the finite variance of the overlap operator in the replica symmetric Gibbs state implies the existence of a spontaneous replica symmetry breaking.