Rounding of First Order Transitions in Low-Dimensional Quantum Systems with Quenched Disorder

TL;DR

This paper rigorously proves that small random perturbations eliminate first order phase transitions in low-dimensional quantum systems, confirming the quantum analogue of the classical Imry-Ma phenomenon.

Contribution

It establishes the first rigorous proof of the Imry-Ma phenomenon for quantum systems in low dimensions, extending classical results to quantum spin models.

Findings

Random perturbations round first order transitions in d <= 2 for quantum systems.

In systems with continuous symmetry, this occurs in d <= 4.

The result confirms the quantum version of the Imry-Ma phenomenon.

Abstract

We prove that the addition of an arbitrarily small random perturbation of a suitable type to a quantum spin system rounds a first order phase transition in the conjugate order parameter in d <= 2 dimensions, or in systems with continuous symmetry in d <= 4. This establishes rigorously for quantum systems the existence of the Imry-Ma phenomenon, which for classical systems was proven by Aizenman and Wehr.