Many-body localization implies that eigenvectors are matrix-product states

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Standard

Many-body localization implies that eigenvectors are matrix-product states. / Friesdorf, M.; Werner, A. H.; Brown, W.; Scholz, V. B.; Eisert, J.

In: Physical Review Letters, Vol. 114, No. 17, 170505, 01.05.2015.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Friesdorf, M, Werner, AH, Brown, W, Scholz, VB & Eisert, J 2015, 'Many-body localization implies that eigenvectors are matrix-product states', Physical Review Letters, vol. 114, no. 17, 170505. https://doi.org/10.1103/PhysRevLett.114.170505

APA

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

Vancouver

Friesdorf M, Werner AH, Brown W, Scholz VB, Eisert J. Many-body localization implies that eigenvectors are matrix-product states. Physical Review Letters. 2015 May 1;114(17). 170505. https://doi.org/10.1103/PhysRevLett.114.170505

Author

Friesdorf, M. ; Werner, A. H. ; Brown, W. ; Scholz, V. B. ; Eisert, J. / Many-body localization implies that eigenvectors are matrix-product states. In: Physical Review Letters. 2015 ; Vol. 114, No. 17.

Bibtex

@article{dd7426fde6814e42b6fa49edd70a93f5,
title = "Many-body localization implies that eigenvectors are matrix-product states",
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.",
author = "M. Friesdorf and Werner, {A. H.} and W. Brown and Scholz, {V. B.} and J. Eisert",
year = "2015",
month = may,
day = "1",
doi = "10.1103/PhysRevLett.114.170505",
language = "English",
volume = "114",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "17",

}

RIS

TY - JOUR

T1 - Many-body localization implies that eigenvectors are matrix-product states

AU - Friesdorf, M.

AU - Werner, A. H.

AU - Brown, W.

AU - Scholz, V. B.

AU - Eisert, J.

PY - 2015/5/1

Y1 - 2015/5/1

N2 - 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.

AB - 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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U2 - 10.1103/PhysRevLett.114.170505

DO - 10.1103/PhysRevLett.114.170505

M3 - Journal article

AN - SCOPUS:84930210951

VL - 114

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

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M1 - 170505

ER -

ID: 236787210