Reentrant Random Quantum Ising Antiferromagnet

TL;DR

This paper investigates the phase diagram of a disordered quantum Ising chain with random couplings and fields, revealing an infinite disorder fixed point, a first-order transition, and a reentrant ordered phase due to quantum fluctuations.

Contribution

It introduces a comprehensive numerical study of the reentrant ordered phase in a disordered quantum Ising model with a longitudinal field, highlighting novel quantum fluctuation effects.

Findings

Identification of an infinite disorder quantum fixed point at zero longitudinal field.

Discovery of a classical first-order transition point at high longitudinal field.

Observation of a reentrant ordered phase driven by quantum fluctuations.

Abstract

We consider the quantum Ising chain with uniformly distributed random antiferromagnetic couplings $(1 \le J_i \le 2)$ and uniformly distributed random transverse fields ($\Gamma_0 \le \Gamma_i \le 2\Gamma_0$) in the presence of a homogeneous longitudinal field, $h$. Using different numerical techniques (DMRG, combinatorial optimisation and strong disorder RG methods) we explore the phase diagram, which consists of an ordered and a disordered phase. At one end of the transition line ($h=0,\Gamma_0=1$) there is an infinite disorder quantum fixed point, while at the other end ($h=2,\Gamma_0=0$) there is a classical random first-order transition point. Close to this fixed point, for $h>2$ and $\Gamma_0>0$ there is a reentrant ordered phase, which is the result of quantum fluctuations by means of an order through disorder phenomenon.