Encoding the structure of many-body localization with matrix product operators

David Pekker, Bryan K. Clark

Research output: Contribution to journalArticle

Abstract

Anderson insulators are noninteracting disordered systems which have localized single-particle eigenstates. The interacting analog of Anderson insulators are the many-body localized (MBL) phases. The spectrum of the many-body eigenstates of an Anderson insulator is efficiently represented as a set of product states over the single-particle modes. We show that product states over matrix product operators of small bond dimension is the corresponding efficient description of the spectrum of an MBL insulator. In this language all of the many-body eigenstates are encoded by matrix product states (i.e., density matrix renormalization group wave functions) consisting of only two sets of low bond dimension matrices per site: the Gi matrices corresponding to the local ground state on site i and the Ei matrices corresponding to the local excited state. All 2n eigenstates can be generated from all possible combinations of these sets of matrices.

Original languageEnglish (US)
Article number035116
JournalPhysical Review B
Volume95
Issue number3
DOIs
StatePublished - Jan 10 2017

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eigenvectors
coding
insulators
operators
products
matrices
wave functions
analogs
ground state
Wave functions
Excited states
Ground state
excitation

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Encoding the structure of many-body localization with matrix product operators. / Pekker, David; Clark, Bryan K.

In: Physical Review B, Vol. 95, No. 3, 035116, 10.01.2017.

Research output: Contribution to journalArticle

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