Phases and phase transitions in disordered quantum systems

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.

Pedagogical introduction to strong disorder physics at quantum phase transitions. Based on lectures given at the XVII Training Course in the Physics of Strongly Correlated Systems in Vietri sul Mare, Italy in October 2012. Submitted to the proceedings of this school. 60 pages and 23 figures. Builds on material reviewed in arXiv:cond-mat/0602312 and arXiv:1005.2707

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