Structure of the entanglement entropy of (3+1)-dimensional gapped phases of matter

doi:https://doi.org/10.1103/physrevb.97.195118

Title: Structure of the entanglement entropy of (3+1)-dimensional gapped phases of matter

Abstract

Not provided.

Authors:: Zheng, Yunqin; He, Huan; Bradlyn, Barry; Cano, Jennifer; Neupert, Titus; Bernevig, B. Andrei

Publication Date:: 2018-05-01

Research Org.:: Princeton Univ., NJ (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1540863

DOE Contract Number:: SC0016239

Resource Type:: Journal Article

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 97; Journal Issue: 19; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: Materials Science; Physics

Citation Formats


                    Zheng, Yunqin, He, Huan, Bradlyn, Barry, Cano, Jennifer, Neupert, Titus, and Bernevig, B. Andrei. Structure of the entanglement entropy of (3+1)-dimensional gapped phases of matter.  United States: N. p., 2018. 
        Web.  doi:10.1103/physrevb.97.195118.

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                    Zheng, Yunqin, He, Huan, Bradlyn, Barry, Cano, Jennifer, Neupert, Titus, & Bernevig, B. Andrei. Structure of the entanglement entropy of (3+1)-dimensional gapped phases of matter.  United States.  https://doi.org/10.1103/physrevb.97.195118

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                    Zheng, Yunqin, He, Huan, Bradlyn, Barry, Cano, Jennifer, Neupert, Titus, and Bernevig, B. Andrei. Tue .  
        "Structure of the entanglement entropy of (3+1)-dimensional gapped phases of matter".  United States.  https://doi.org/10.1103/physrevb.97.195118.

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@article{osti_1540863,

  title        = {Structure of the entanglement entropy of (3+1)-dimensional gapped phases of matter},

  author       = {Zheng, Yunqin and He, Huan and Bradlyn, Barry and Cano, Jennifer and Neupert, Titus and Bernevig, B. Andrei},

  abstractNote = {Not provided.},

  doi          = {10.1103/physrevb.97.195118},

  url          = {https://www.osti.gov/biblio/1540863},
  journal      = {Physical Review B},

  issn         = {2469-9950},

  number       = 19,

  volume       = 97,

  place        = {United States},

  year         = {2018},

  month        = {5}

}

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Title: Structure of the entanglement entropy of (3+1)-dimensional gapped phases of matter

Abstract

Citation Formats

Symmetry-Protected Topological Phases of Quantum Matter journal, March 2015

Quantized Hall conductivity in two dimensions journal, May 1981

Two-Dimensional Magnetotransport in the Extreme Quantum Limit journal, May 1982

Topological Orders in Rigid States journal, February 1990

Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State journal, April 1983

Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model journal, February 1983

Quantum Spin Hall Effect in Graphene journal, November 2005

Quantum Spin Hall Effect journal, March 2006

Symmetry protected topological orders and the group cohomology of their symmetry group journal, April 2013

Topological insulators and superconductors: tenfold way and dimensional hierarchy journal, June 2010

Topological Crystalline Insulators journal, March 2011

Hourglass fermions journal, April 2016

Topological Insulators from Group Cohomology journal, April 2016

Classification of Abelian quantum Hall states and matrix formulation of topological fluids journal, July 1992

Excitation structure of the hierarchy scheme in the fractional quantum Hall effect journal, September 1990

Theory and classification of interacting integer topological phases in two dimensions: A Chern-Simons approach journal, September 2012

Classification and properties of symmetry-enriched topological phases: Chern-Simons approach with applications to Z 2 spin liquids journal, April 2016

A classification of quantum Hall fluids journal, February 1997

Anyons in an exactly solved model and beyond journal, January 2006

Interferometry of non-Abelian anyons journal, November 2008

Topological orders and edge excitations in fractional quantum Hall states journal, October 1995

Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect journal, February 2013

Gapped boundary phases of topological insulators via weak coupling journal, November 2016

Anomalous Discrete Symmetries in Three Dimensions and Group Cohomology journal, June 2014

Field theories for gauged symmetry-protected topological phases: Non-Abelian anyons with Abelian gauge group Z 2 ⊗ 3 journal, January 2017

Braiding statistics approach to symmetry-protected topological phases journal, September 2012

Anomalies and fermion zero modes on strings and domain walls journal, January 1985

Topological Insulators in Three Dimensions journal, March 2007

Exactly soluble model of a three-dimensional symmetry-protected topological phase of bosons with surface topological order journal, December 2014

Anomalous Symmetry Fractionalization and Surface Topological Order journal, October 2015

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Symmetry-respecting topologically ordered surface phase of three-dimensional electron topological insulators journal, September 2015

Bosonic topological insulator in three dimensions and the statistical Witten effect journal, July 2013

Nonabelions in the fractional quantum hall effect journal, August 1991

Fractional Statistics and the Quantum Hall Effect journal, August 1984

Braiding Statistics of Loop Excitations in Three Dimensions journal, August 2014

Non-Abelian string and particle braiding in topological order: Modular SL ( 3 , Z ) representation and ( 3 + 1 ) -dimensional twisted gauge theory journal, January 2015

Braiding statistics and link invariants of bosonic/fermionic topological quantum matter in 2+1 and 3+1 dimensions journal, September 2017

Topological Entanglement Entropy journal, March 2006

Detecting Topological Order in a Ground State Wave Function journal, March 2006

Topological entanglement entropy of a Bose–Hubbard spin liquid journal, July 2011

Identifying topological order by entanglement entropy journal, November 2012

Nature of the Spin-Liquid Ground State of the S = 1 / 2 Heisenberg Model on the Kagome Lattice journal, August 2012

Topological order in a three-dimensional toric code at finite temperature journal, October 2008

Three-dimensional topological lattice models with surface anyons journal, January 2013

Entropic manifestations of topological order in three dimensions journal, March 2016

Entanglement entropy of gapped phases and topological order in three dimensions journal, November 2011

Holographic entropy inequalities and gapped phases of matter journal, September 2015

Entropy inequalities journal, June 1970

Quantum error correction for beginners journal, June 2013

The holographic entropy cone journal, September 2015

(3+1)-TQFTs and topological insulators journal, July 2011

Generalized global symmetries journal, February 2015

Coupling a QFT to a TQFT and duality journal, April 2014

Quantum field theory and the Jones polynomial journal, September 1989

Remarks on the canonical quantization of the Chern-Simons-Witten theory journal, October 1989

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A refinement of entanglement entropy and the number of degrees of freedom journal, April 2013

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Entanglement entropy from tensor network states for stabilizer codes journal, March 2018

Observations on entanglement entropy in massive QFT’s journal, April 2013

Symmetry-Protected Topological Phases of Quantum Matter
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Quantized Hall conductivity in two dimensions
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Two-Dimensional Magnetotransport in the Extreme Quantum Limit
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Topological Orders in Rigid States
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Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State
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Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model
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Quantum Spin Hall Effect in Graphene
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Quantum Spin Hall Effect
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Symmetry protected topological orders and the group cohomology of their symmetry group
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Topological insulators and superconductors: tenfold way and dimensional hierarchy
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Topological Crystalline Insulators
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Hourglass fermions
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Topological Insulators from Group Cohomology
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Classification of Abelian quantum Hall states and matrix formulation of topological fluids
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Excitation structure of the hierarchy scheme in the fractional quantum Hall effect
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Theory and classification of interacting integer topological phases in two dimensions: A Chern-Simons approach
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Classification and properties of symmetry-enriched topological phases: Chern-Simons approach with applications to $Z_{2}$ spin liquids
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A classification of quantum Hall fluids
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Anyons in an exactly solved model and beyond
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Interferometry of non-Abelian anyons
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Topological orders and edge excitations in fractional quantum Hall states
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Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect
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Gapped boundary phases of topological insulators via weak coupling
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Anomalous Discrete Symmetries in Three Dimensions and Group Cohomology
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Field theories for gauged symmetry-protected topological phases: Non-Abelian anyons with Abelian gauge group $Z_{2}^{\otimes 3}$
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Braiding statistics approach to symmetry-protected topological phases
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Anomalies and fermion zero modes on strings and domain walls
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Topological Insulators in Three Dimensions
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Exactly soluble model of a three-dimensional symmetry-protected topological phase of bosons with surface topological order
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Anomalous Symmetry Fractionalization and Surface Topological Order
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Symmetry enforced non-Abelian topological order at the surface of a topological insulator
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Symmetry-respecting topologically ordered surface phase of three-dimensional electron topological insulators
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Bosonic topological insulator in three dimensions and the statistical Witten effect
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Nonabelions in the fractional quantum hall effect
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Fractional Statistics and the Quantum Hall Effect
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Braiding Statistics of Loop Excitations in Three Dimensions
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Non-Abelian string and particle braiding in topological order: Modular $SL (3, Z)$ representation and $(3 + 1)$ -dimensional twisted gauge theory
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Braiding statistics and link invariants of bosonic/fermionic topological quantum matter in 2+1 and 3+1 dimensions
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Topological Entanglement Entropy
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Detecting Topological Order in a Ground State Wave Function
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Topological entanglement entropy of a Bose–Hubbard spin liquid
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Identifying topological order by entanglement entropy
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Nature of the Spin-Liquid Ground State of the $S = 1 / 2$ Heisenberg Model on the Kagome Lattice
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Topological order in a three-dimensional toric code at finite temperature
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Three-dimensional topological lattice models with surface anyons
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Entropic manifestations of topological order in three dimensions
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Entanglement entropy of gapped phases and topological order in three dimensions
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Holographic entropy inequalities and gapped phases of matter
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Entropy inequalities
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Quantum error correction for beginners
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The holographic entropy cone
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(3+1)-TQFTs and topological insulators
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Generalized global symmetries
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Coupling a QFT to a TQFT and duality
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Quantum field theory and the Jones polynomial
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Remarks on the canonical quantization of the Chern-Simons-Witten theory
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Fault-tolerant quantum computation by anyons
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Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions
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Entanglement spectrum of a topological phase in one dimension
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Topological phases of one-dimensional fermions: An entanglement point of view
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Inversion-symmetric topological insulators
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Entanglement spectrum classification of $C_{n}$ -invariant noninteracting topological insulators in two dimensions
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Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
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Topological Entanglement and Clustering of Jain Hierarchy States
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Bulk-edge correspondence in entanglement spectra
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Real-space entanglement spectrum of quantum Hall systems
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Edge-state inner products and real-space entanglement spectrum of trial quantum Hall states
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Real-space entanglement spectrum of quantum Hall states
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Correlation Lengths and Topological Entanglement Entropies of Unitary and Nonunitary Fractional Quantum Hall Wave Functions
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Zoology of fractional Chern insulators
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A refinement of entanglement entropy and the number of degrees of freedom
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Probing renormalization group flows using entanglement entropy
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Local stabilizer codes in three dimensions without string logical operators
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Topological entanglement entropy of fracton stabilizer codes
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Entanglement entropy from tensor network states for stabilizer codes
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Observations on entanglement entropy in massive QFT’s
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