The de Almeida-Thouless Line in Hierarchical Quantum Spin Glasses

TL;DR

This paper investigates the effects of combined longitudinal and transversal magnetic fields on the phases of hierarchical quantum spin glasses, extending classical and quantum results and highlighting the phase shrinking due to magnetic fields.

Contribution

It explicitly analyzes the joint effects of magnetic fields on the Quantum GREM, extending classical and quantum phase results, and proposes a hierarchical implementation of the longitudinal field.

Findings

Magnetic fields cause the spin glass phase to shrink.

Hierarchical implementation of the longitudinal field is necessary.

Results extend classical and quantum phase diagrams.

Abstract

We determine explicitly and discuss in detail the effects of the joint presence of a longitudinal and a transversal (random) magnetic field on the phases of the Random Energy Model (REM) and its hierarchical generalization, the GREM. Our results extent known results both in the classical case of vanishing transversal field and in the quantum case for vanishing longitudinal field. Following Derrida and Gardner, we argue that the longitudinal field has to be implemented hierarchically also in the Quantum GREM. We show that this ensures the shrinking of the spin glass phase in the presence of the magnetic fields as also expected for the Quantum Sherrington-Kirkpatrick model.