Cavity method for quantum spin glasses on the Bethe lattice

TL;DR

This paper extends the cavity method to quantum spin glasses on Bethe lattices, enabling analysis of their phase structure and observable distributions, with implications for quantum computation.

Contribution

It introduces a generalized cavity method for quantum spin glasses on fixed connectivity lattices, advancing tools for quantum statistical physics.

Findings

Numerical solution of the phase diagram for a q=3 transverse field Ising model.

Analysis of the distribution of classical and quantum observables.

Insights into the quantum phase transitions on Bethe lattices.

Abstract

We propose a generalization of the cavity method to quantum spin glasses on fixed connectivity lattices. Our work is motivated by the recent refinements of the classical technique and its potential application to quantum computational problems. We numerically solve for the phase structure of a connectivity $q=3$ transverse field Ising model on a Bethe lattice with $\pm J$ couplings, and investigate the distribution of various classical and quantum observables.