Stability of the quantum Sherrington-Kirkpatrick spin glass model

TL;DR

This paper investigates the quantum SK spin glass model, revealing the instability of the replica symmetric solution at all temperatures and identifying a quantum de Almeida-Thouless line, which could impact quantum annealing performance.

Contribution

It provides the first detailed numerical analysis showing the instability of the RS solution at zero temperature and identifies a quantum AT line in the phase diagram.

Findings

Replica symmetric solution is unstable down to zero temperature.

Existence of a quantum de Almeida-Thouless (QuAT) line at T=0.

Implications for quantum annealers solving spin glass problems.

Abstract

We study in detail the quantum Sherrington-Kirkpatrick (SK) model, i.e. the infinite-range Ising spin glass in a transverse field, by solving numerically the effective one-dimensional model that the quantum SK model can be mapped to in the thermodynamic limit. We find that the replica symmetric (RS) solution is unstable down to zero temperature, in contrast to some previous claims, and so there is not only a line of transitions in the (longitudinal) field-temperature plane (the de Almeida-Thouless, AT, line) where replica symmetry is broken, but also a quantum de Almeida-Thouless (QuAT) line in the transverse field-longitudinal field plane at $T = 0$. If the QuAT line also occurs in models with short-range interactions its presence might affect the performance of quantum annealers when solving spin glass-type problems with a bias (i.e. magnetic field).