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Title: Entanglement spectrum of a random partition: Connection with the localization transition

Abstract

We study the entanglement spectrum of a translationally invariant lattice system under a random partition, implemented by choosing each site to be in one subsystem with probability pϵ[0,1]. We apply this random partitioning to a translationally invariant (i.e., clean) topological state, and argue on general grounds that the corresponding entanglement spectrum captures the universal behavior about its disorder-driven transition to a trivial localized phase. Specifically, as a function of the partitioning probability p, the entanglement Hamiltonian HA must go through a topological phase transition driven by the percolation of a random network of edge states. For example, we analytically derive the entanglement Hamiltonian for a one-dimensional topological superconductor under a random partition, and demonstrate that its phase diagram includes transitions between Griffiths phases. We discuss potential advantages of studying disorder-driven topological phase transitions via the entanglement spectra of random partitions.

Authors:
 [1];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
OSTI Identifier:
1505793
Alternate Identifier(s):
OSTI ID: 1184683
Grant/Contract Number:  
SC0010526
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 91; Journal Issue: 22; Journal ID: ISSN 1098-0121
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Vijay, Sagar, and Fu, Liang. Entanglement spectrum of a random partition: Connection with the localization transition. United States: N. p., 2015. Web. doi:10.1103/physrevb.91.220101.
Vijay, Sagar, & Fu, Liang. Entanglement spectrum of a random partition: Connection with the localization transition. United States. doi:10.1103/physrevb.91.220101.
Vijay, Sagar, and Fu, Liang. Mon . "Entanglement spectrum of a random partition: Connection with the localization transition". United States. doi:10.1103/physrevb.91.220101. https://www.osti.gov/servlets/purl/1505793.
@article{osti_1505793,
title = {Entanglement spectrum of a random partition: Connection with the localization transition},
author = {Vijay, Sagar and Fu, Liang},
abstractNote = {We study the entanglement spectrum of a translationally invariant lattice system under a random partition, implemented by choosing each site to be in one subsystem with probability pϵ[0,1]. We apply this random partitioning to a translationally invariant (i.e., clean) topological state, and argue on general grounds that the corresponding entanglement spectrum captures the universal behavior about its disorder-driven transition to a trivial localized phase. Specifically, as a function of the partitioning probability p, the entanglement Hamiltonian HA must go through a topological phase transition driven by the percolation of a random network of edge states. For example, we analytically derive the entanglement Hamiltonian for a one-dimensional topological superconductor under a random partition, and demonstrate that its phase diagram includes transitions between Griffiths phases. We discuss potential advantages of studying disorder-driven topological phase transitions via the entanglement spectra of random partitions.},
doi = {10.1103/physrevb.91.220101},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 22,
volume = 91,
place = {United States},
year = {2015},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

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Cited by: 8 works
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Figures / Tables:

FIG. 1 FIG. 1: The two ground states of the Kitaev p-wave superconductor with dimerization of Majorana fermions across (top) and within (bottom) lattice sites, corresponding to a TSC and a trivial p-wave superconductor, respectively.

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Works referenced in this record:

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    Figures / Tables found in this record:

      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.