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

Vijay, Sagar; Fu, Liang

doi:10.1103/physrevb.91.220101

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

Journal Article · Mon Jun 15 00:00:00 EDT 2015 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/physrevb.91.220101· OSTI ID:1505793

Vijay, Sagar ^[1]; Fu, Liang ^[1]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

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 H_A 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.

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Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE

Grant/Contract Number:: SC0010526

OSTI ID:: 1505793

Alternate ID(s):: OSTI ID: 1184683

Journal Information:: Physical Review. B, Condensed Matter and Materials Physics, Vol. 91, Issue 22; ISSN 1098-0121

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 12 works

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Cited By (3)

Learning phase transitions by confusion van Nieuwenburg, Evert P. L.; Liu, Ye-Hua; Huber, Sebastian D. Nature Physics, Vol. 13, Issue 5 https://doi.org/10.1038/nphys4037	journal	February 2017
Analytic expression for the entanglement entropy of a two-dimensional topological superconductor Borchmann, Jan; Pereg-Barnea, T. Physical Review B, Vol. 95, Issue 7 https://doi.org/10.1103/physrevb.95.075152	journal	February 2017
Learning phase transitions by confusion van Nieuwenburg, Evert P. L.; Liu, Ye-Hua; Huber, Sebastian D. arXiv https://doi.org/10.48550/arxiv.1610.02048	text	January 2016

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