A Novel Quantum Transition in a Fully Frustrated Transverse Ising Antiferromagnet

TL;DR

This paper investigates the effects of quantum and thermal fluctuations on a fully frustrated long-range Ising antiferromagnet, revealing a novel phase transition to a spin glass order induced by infinitesimal disorder.

Contribution

It introduces a new phase transition in a fully frustrated long-range Ising antiferromagnet caused by small disorder, quantum, or thermal fluctuations, and discusses implications for studying spin glass phases.

Findings

Antiferromagnetic order is immediately broken by quantum or thermal fluctuations.

Infinitesimal disorder induces a stable spin glass phase in the antiferromagnet.

Transition to paramagnetic phase occurs at higher fluctuations.

Abstract

We consider a long-range Ising antiferromagnet (LRIAF) put in a transverse field. Applying quantum Monte Carlo method, we study the variation of order parameter (spin correlation in Trotter time direction), susceptibility and average energy of the system for various values of the transverse field at different temperatures. The antiferromagnetic order is seen to get immediately broken as soon as the thermal or quantum fluctuations are added. We also discuss the phase diagram for the Sherrington-Kirkpatrick (SK) model with the same LRIAF bias, also in presence of a transverse field. We find that while the antiferromagnetic order is immediately broken as one adds an infinitesimal transverse field or thermal fluctuation to the system, an infinitesimal SK spin glass disorder is enough to induce a stable glass order in the antiferromagnet. This glass order eventually gets destroyed as the thermal or quantum fluctuations increased beyond their threshold values and the transition to para phase occurs. Indications of this novel phase transition are discussed. Because of the presence of full frustration, this surrogate property of the LRIAF for incubation of stable spin glass phase in it (induced by addition of a small disorder) should enable eventually the study of classical and quantum spin glass phases by using some perturbation theory with respect to the disorder.