Hall conductance and the statistics of flux insertions in gapped interacting lattice systems

Kapustin, Anton; Sopenko, Nikita

doi:10.1063/5.0022944

Title: Hall conductance and the statistics of flux insertions in gapped interacting lattice systems

Abstract

We study charge transport for zero-temperature infinite-volume gapped lattice systems in two dimensions with short-range interactions. We show that the Hall conductance is locally computable and is the same for all systems that are in the same gapped phase. Here, we provide a rigorous version of Laughlin’s flux-insertion argument, which shows that for short-range entangled systems, the Hall conductance is an integer multiple of e²/h. We show that the Hall conductance determines the statistics of flux insertions. For bosonic short-range entangled systems, this implies that the Hall conductance is an even multiple of e²/h. Finally, we adapt a proof of quantization of the Thouless charge pump to the case of infinite-volume gapped lattice systems in one dimension.

Authors:

^[1];

^[1]

California Institute of Technology (CalTech), Pasadena, CA (United States)

Publication Date:: Thu Oct 01 00:00:00 EDT 2020

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1851488

Alternate Identifier(s):: OSTI ID: 1669162

Grant/Contract Number:: SC0011632

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Mathematical Physics

Additional Journal Information:: Journal Volume: 61; Journal Issue: 10; Journal ID: ISSN 0022-2488

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Boson systems; charge transport; Goldstone theorem; quantum Hall effect; fermion systems

Citation Formats


                    Kapustin, Anton, and Sopenko, Nikita. Hall conductance and the statistics of flux insertions in gapped interacting lattice systems.  United States: N. p., 2020. 
Web.  doi:10.1063/5.0022944.

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                    Kapustin, Anton, & Sopenko, Nikita. Hall conductance and the statistics of flux insertions in gapped interacting lattice systems.  United States.  https://doi.org/10.1063/5.0022944

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                    Kapustin, Anton, and Sopenko, Nikita. Thu .  
"Hall conductance and the statistics of flux insertions in gapped interacting lattice systems".  United States.  https://doi.org/10.1063/5.0022944.  https://www.osti.gov/servlets/purl/1851488.

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@article{osti_1851488,

  title        = {Hall conductance and the statistics of flux insertions in gapped interacting lattice systems},

  author       = {Kapustin, Anton and Sopenko, Nikita},

  abstractNote = {We study charge transport for zero-temperature infinite-volume gapped lattice systems in two dimensions with short-range interactions. We show that the Hall conductance is locally computable and is the same for all systems that are in the same gapped phase. Here, we provide a rigorous version of Laughlin’s flux-insertion argument, which shows that for short-range entangled systems, the Hall conductance is an integer multiple of e2/h. We show that the Hall conductance determines the statistics of flux insertions. For bosonic short-range entangled systems, this implies that the Hall conductance is an even multiple of e2/h. Finally, we adapt a proof of quantization of the Thouless charge pump to the case of infinite-volume gapped lattice systems in one dimension.},

  doi          = {10.1063/5.0022944},

  journal      = {Journal of Mathematical Physics},

  number       = 10,

  volume       = 61,

  place        = {United States},

  year         = {Thu Oct 01 00:00:00 EDT 2020},

  month        = {Thu Oct 01 00:00:00 EDT 2020}

}

Copy to clipboard

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Works referenced in this record:

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Similar Records

Title: Hall conductance and the statistics of flux insertions in gapped interacting lattice systems

Abstract

Citation Formats

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

Spectral Gap and Exponential Decay of Correlations journal, April 2006

A Many-Body Index for Quantum Charge Transport journal, July 2019

Boundedness of Entanglement Entropy and Split Property of Quantum spin Chains journal, October 2013

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The noncommutative geometry of the quantum Hall effect journal, October 1994

Quantization of Conductance in Gapped Interacting Systems journal, February 2018

Lieb-Robinson Bounds and the Exponential Clustering Theorem journal, March 2006

Propagation of Correlations in Quantum Lattice Systems journal, July 2006

Many-body Fredholm index for ground-state spaces and Abelian anyons journal, February 2020

Local Quantum Physics book, January 1996

Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems journal, November 2011

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Quantised adiabatic charge transport in the presence of substrate disorder and many-body interaction journal, August 1984

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Quantization of the Hall Conductance for General, Multiparticle Schrödinger Hamiltonians journal, January 1985

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

Spectral Gap and Exponential Decay of Correlations
journal, April 2006

A Many-Body Index for Quantum Charge Transport
journal, July 2019

Boundedness of Entanglement Entropy and Split Property of Quantum spin Chains
journal, October 2013

Automorphic equivalence within gapped phases in the bulk
journal, May 2020

Quantization of Hall Conductance for Interacting Electrons on a Torus
journal, September 2014

Quantization of the Hall Conductance for General, Multiparticle Schrödinger Hamiltonians
journal, January 1985

The noncommutative geometry of the quantum Hall effect
journal, October 1994

Quantization of Conductance in Gapped Interacting Systems
journal, February 2018

Lieb-Robinson Bounds and the Exponential Clustering Theorem
journal, March 2006

Propagation of Correlations in Quantum Lattice Systems
journal, July 2006

Many-body Fredholm index for ground-state spaces and Abelian anyons
journal, February 2020

Local Quantum Physics
book, January 1996

Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
journal, November 2011

Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems
journal, January 2020

Quantised adiabatic charge transport in the presence of substrate disorder and many-body interaction
journal, August 1984

Higher-dimensional generalizations of Berry curvature
journal, June 2020

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journal, January 1985