Disorder in Quantum Many-Body Systems


Impurities, defects, and other types of imperfections are ubiquitous in realistic quantum many-body systems and essentially unavoidable in solid state materials. Often, such random disorder is viewed purely negatively as it is believed to prevent interesting new quantum states of matter from forming and to smear out sharp features associated with the phase transitions between them. However, disorder is also responsible for a variety of interesting novel phenomena that do not have clean counterparts. These include Anderson localization of single-particle wave functions, many-body localization in isolated many-body systems, exotic quantum critical points, and glassy ground-state phases. This brief review focuses on two separate but related subtopics in this field. First, we review under what conditions different types of randomness affect the stability of symmetry-broken low-temperature phases in quantum many-body systems and the stability of the corresponding phase transitions. Second, we discuss the fate of quantum phase transitions that are destabilized by disorder as well as the unconventional quantum Griffiths phases that emerge in their vicinity.



Research Center/Lab(s)

Center for High Performance Computing Research


National Science Foundation (U.S.)


This work was supported in part by the NSF under Grant Nos. PHY-1125915 and DMR-1506152.

Keywords and Phrases

Disorder; Griffiths phases; Griffiths singularities; Quantum phase transitions; Randomness; Rare regions; Symmetry breaking

International Standard Serial Number (ISSN)

1947-5454; 1947-5462

Document Type

Article - Journal

Document Version


File Type





© 2019 Annual Reviews Inc., All rights reserved.

Publication Date

01 Mar 2019