Exactly solvable quantum spin-glass model with 1RSB-fullRSB transition

TL;DR

This paper introduces an exactly solvable quantum spin-glass model that exhibits a transition from one-step to full replica symmetry breaking, providing insights into quantum phase transitions in disordered systems.

Contribution

The authors derive an exact free energy expression for a new quantum spin-glass model, demonstrating a 1RSB-fullRSB transition at low temperatures, and show the method's applicability to classical models.

Findings

Existence of a 1RSB-fullRSB transition at low temperatures.

Exact free energy expression for the quantum spin-glass model.

Method applicable to classical spin models to find quantum counterparts.

Abstract

We introduce a novel quantum spin-glass model, a Sherrington-Kirkpatrick model with a transverse mean-field type random magnet. We rigorously derive the exact expression of the free energy of this model at the entire parameter region. The obtained exact solution implies the existence of a 1RSB-fullRSB transition at low temperatures. Our technique can be applied to general classical spin models, telling that any solvable classical spin model has its solvable quantum counterpart.