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

TL;DR

This paper proves that quenched disorder eliminates first order phase transitions in low-dimensional quantum systems, extending the classical Imry-Ma phenomenon to quantum contexts by analyzing thermodynamic quantities.

Contribution

It establishes the quantum analog of the Imry-Ma phenomenon, showing disorder rounds phase transitions in low-dimensional quantum lattice systems, with an extension to systems with continuous symmetry.

Findings

Disorder rounds first order transitions in d<=2 quantum systems.

Extension of the phenomenon to d<=4 for systems with continuous symmetry.

Analysis based on thermodynamic quantities rather than equilibrium states.

Abstract

We prove that for quantum lattice systems in d<=2 dimensions the addition of quenched disorder rounds any first order phase transition in the corresponding conjugate order parameter, both at positive temperatures and at T=0. For systems with continuous symmetry the statement extends up to d<=4 dimensions. This establishes for quantum systems the existence of the Imry-Ma phenomenon which for classical systems was proven by Aizenman and Wehr. The extension of the proof to quantum systems is achieved by carrying out the analysis at the level of thermodynamic quantities rather than equilibrium states.