On the quantum spin glass transition on the Bethe lattice

TL;DR

This paper studies the quantum phase transition in a disordered Ising model on the Bethe lattice, identifying the transition point and exploring the nature of the glassy phase using numerical and mean-field methods.

Contribution

It combines quantum Monte Carlo, exact diagonalization, and mean-field theory to analyze the quantum spin glass transition on the Bethe lattice, revealing particle delocalization at the transition.

Findings

Transition point identified via Rènyi entropy peak

Particles are delocalized at the transition

Potential for a many-body localized phase deep in the glassy state

Abstract

We investigate the ground-state properties of a disorderd Ising model with uniform transverse field on the Bethe lattice, focusing on the quantum phase transition from a paramagnetic to a glassy phase that is induced by reducing the intensity of the transverse field. We use a combination of quantum Monte Carlo algorithms and exact diagonalization to compute R\'enyi entropies, quantum Fisher information, correlation functions and order parameter. We locate the transition by means of the peak of the R\'enyi entropy and we find agreement with the transition point estimated from the emergence of finite values of the Edwards-Anderson order parameter and from the peak of the correlation length. We interpret the results by means of a mean-field theory in which quantum fluctuations are treated as massive particles hopping on the interaction graph. We see that the particles are delocalized at the transition, a fact that points towards the existence of possibly another transition deep in the glassy phase where these particles localize, therefore leading to a many-body localized phase.