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

Journal Article · · Physical Review. B, Condensed Matter and Materials Physics
 [1];  [2]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
+ Show Author Affiliations
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.
Research Organization:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
Grant/Contract Number:
SC0010526
OSTI ID:
1505793
Alternate ID(s):
OSTI ID: 1184683
Journal Information:
Physical Review. B, Condensed Matter and Materials Physics, Journal Name: Physical Review. B, Condensed Matter and Materials Physics Journal Issue: 22 Vol. 91; ISSN 1098-0121; ISSN PRBMDO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Cited By (3)

Learning phase transitions by confusion journal February 2017
Analytic expression for the entanglement entropy of a two-dimensional topological superconductor journal February 2017
Learning phase transitions by confusion text January 2016

Figures / Tables (2)

FIG. 1(p. 3)figure FIG. 1
FIG. 2(p. 4)figure FIG. 2

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71 CLASSICAL AND QUANTUM MECHANICS
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