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Friesdorf M, Werner AH, Brown W, et al. Many-Body Localization Implies that Eigenvectors are Matrix-Product States. Phys Rev Lett. 2015;114(17):170505doi: 10.1103/PhysRevLett.114.170505.
Friesdorf, M., Werner, A. H., Brown, W., Scholz, V. B., & Eisert, J. (2015). Many-Body Localization Implies that Eigenvectors are Matrix-Product States. Physical review letters, 114(17), 170505. https://doi.org/10.1103/PhysRevLett.114.170505
Friesdorf, M, et al. "Many-Body Localization Implies that Eigenvectors are Matrix-Product States." Physical review letters vol. 114,17 (2015): 170505. doi: https://doi.org/10.1103/PhysRevLett.114.170505
Friesdorf M, Werner AH, Brown W, Scholz VB, Eisert J. Many-Body Localization Implies that Eigenvectors are Matrix-Product States. Phys Rev Lett. 2015 May 01;114(17):170505. doi: 10.1103/PhysRevLett.114.170505. Epub 2015 May 01. PMID: 25978216.
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Phys Rev Lett. 2015 May 01;114(17):170505. doi: 10.1103/PhysRevLett.114.170505. Epub 2015 May 01.

Many-Body Localization Implies that Eigenvectors are Matrix-Product States.

Physical review letters

M Friesdorf, A H Werner, W Brown, V B Scholz, J Eisert

Affiliations

  1. Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.
  2. Computer Science Department, University College London, London WC1E 6BT, United Kingdom.
  3. Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland.

PMID: 25978216 DOI: 10.1103/PhysRevLett.114.170505

Abstract

The phenomenon of many-body localization has received a lot of attention recently, both for its implications in condensed-matter physics of allowing systems to be an insulator even at nonzero temperature as well as in the context of the foundations of quantum statistical mechanics, providing examples of systems showing the absence of thermalization following out-of-equilibrium dynamics. In this work, we establish a novel link between dynamical properties--a vanishing group velocity and the absence of transport--with entanglement properties of individual eigenvectors. For systems with a generic spectrum, we prove that strong dynamical localization implies that all of its many-body eigenvectors have clustering correlations. The same is true for parts of the spectrum, thus allowing for the existence of a mobility edge above which transport is possible. In one dimension these results directly imply an entanglement area law; hence, the eigenvectors can be efficiently approximated by matrix-product states.

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