Many-body localization: Concepts and simple models

Robert J Sims, G. Stolz

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

We review recent results on many-body localization for two explicitly analyzable models of many-body quantum systems, the XY spin chain in transversal magnetic field as well as interacting systems of harmonic quantum oscillators. In both models the presence of disorder leads to dynamical localization in the form of zero-velocity Lieb - Robinson bounds and to exponential decay of ground state correlations. Moreover, for oscillator systems one can also show exponential decay of thermal states as well as an area law bound for the entanglement entropy of ground and thermal states. The key fact which allows a rigorous analysis of these models is that they are given by many-body Hamiltonians which can be reduced to effective single particle Hamiltonians.

Original languageEnglish (US)
Pages (from-to)791-822
Number of pages32
JournalMarkov Processes and Related Fields
Volume21
Issue number3P
StatePublished - 2015

Keywords

  • Area law
  • Lieb - Robinson bounds
  • Many-body localization
  • Quantum oscillator systems
  • XY spin chain

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability

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