Many-body localization and thermalization in quantum statistical mechanics

Rahul Nandkishore, David A. Huse

Research output: Contribution to journalReview articlepeer-review

1702 Scopus citations


We review some recent developments in the statistical mechanics of isolated quantum systems. We provide a brief introduction to quantum thermalization, paying particular attention to the eigenstate thermalization hypothesis (ETH) and the resulting single-eigenstate statistical mechanics. We then focus on a class of systems that fail to quantum thermalize and whose eigenstates violate the ETH: These are the many-body Anderson-localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics. These systems can forever locally remember ormation about their local initial conditions and are thus of interest for possibilities of storing quantum ormation. We discuss key features of many-body localization (MBL) and review a phenomenology of the MBL phase. Single-eigenstate statistical mechanics within the MBL phase reveal dynamically stable ordered phases, and phase transitions among them, that are invisible to equilibrium statistical mechanics and can occur at high energy and low spatial dimensionality, where equilibrium ordering is forbidden.

Original languageEnglish (US)
Pages (from-to)15-38
Number of pages24
JournalAnnual Review of Condensed Matter Physics
Issue number1
StatePublished - Mar 10 2015

All Science Journal Classification (ASJC) codes

  • General Materials Science
  • Condensed Matter Physics


  • closed systems
  • eigenstate
  • entanglement
  • glass
  • nonequilibrium


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