Existence of replica-symmetry breaking in quantum glasses

TL;DR

This paper rigorously demonstrates the existence of a spin-glass phase in quantum glasses, specifically in the quantum Sherrington-Kirkpatrick model with a transverse field, under low temperature and field conditions.

Contribution

It provides the first rigorous proof of replica-symmetry breaking in quantum glasses using the Falk-Bruch inequality.

Findings

Existence of spin-glass phase in quantum SK model established

Applicable to generalized transverse p-spin models

Rigorous mathematical proof provided

Abstract

By controlling quantum fluctuations via the Falk-Bruch inequality we give the first rigorous argument for the existence of a spin-glass phase in the quantum Sherrington-Kirkpatrick model with a transverse magnetic field if the temperature and the field are sufficiently low. The argument also applies to the generalization of the model with multi-spin interactions, sometimes dubbed as transverse $p$-spin model.