Phases and phase transitions in disordered quantum systems

TL;DR

This paper provides a pedagogical overview of phase transitions in disordered quantum systems, focusing on exotic phenomena like Griffiths phases, infinite-randomness criticality, and the effects of disorder on phase transition properties.

Contribution

It introduces the strong-disorder renormalization group method and discusses conditions under which disorder alters phase transition behavior, including experimental examples.

Findings

Identification of conditions for disorder-induced changes in phase transitions

Explanation of exotic phenomena like Griffiths phases and infinite-randomness criticality

Presentation of experimental evidence supporting theoretical concepts

Abstract

These lecture notes give a pedagogical introduction to phase transitions in disordered quantum systems and to the exotic Griffiths phases induced in their vicinity. We first review some fundamental concepts in the physics of phase transitions. We then derive criteria governing under what conditions spatial disorder or randomness can change the properties of a phase transition. After introducing the strong-disorder renormalization group method, we discuss in detail some of the exotic phenomena arising at phase transitions in disordered quantum systems. These include infinite-randomness criticality, rare regions and quantum Griffiths singularities, as well as the smearing of phase transitions. We also present a number of experimental examples.