Absence of Energy Currents in an Equilibrium State and Chiral Anomalies

Kapustin, Anton; Spodyneiko, Lev

doi:10.1103/PhysRevLett.123.060601

Title: Absence of Energy Currents in an Equilibrium State and Chiral Anomalies

Abstract

Previously, Bloch showed that in a system of interacting nonrelativistic particles the net particle-number current must vanish in any equilibrium state. Bloch’s argument does not generalize easily to the energy current. We devise an alternative argument which proves the vanishing of the net energy currents in equilibrium states of lattice systems as well as systems of nonrelativistic particles with finite-range potential interactions. We discuss some applications of these results. Specifically, we show that neither a one-dimensional (1D) lattice system nor a 1D system of nonrelativistic particles with finite-range potential interactions can flow to a conformal field theory with unequal left-moving and right-moving central charges.

Authors:

Kapustin, Anton ^[1]; Spodyneiko, Lev ^[1]

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

Publication Date:: Tue Aug 06 00:00:00 EDT 2019

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

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

OSTI Identifier:: 1600555

Alternate Identifier(s):: OSTI ID: 1547989

Grant/Contract Number:: SC0011632

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Volume: 123; Journal Issue: 6; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats


                    Kapustin, Anton, and Spodyneiko, Lev. Absence of Energy Currents in an Equilibrium State and Chiral Anomalies.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevLett.123.060601.

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                    Kapustin, Anton, & Spodyneiko, Lev. Absence of Energy Currents in an Equilibrium State and Chiral Anomalies.  United States.  https://doi.org/10.1103/PhysRevLett.123.060601

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                    Kapustin, Anton, and Spodyneiko, Lev. Tue .  
"Absence of Energy Currents in an Equilibrium State and Chiral Anomalies".  United States.  https://doi.org/10.1103/PhysRevLett.123.060601.  https://www.osti.gov/servlets/purl/1600555.

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@article{osti_1600555,

  title        = {Absence of Energy Currents in an Equilibrium State and Chiral Anomalies},

  author       = {Kapustin, Anton and Spodyneiko, Lev},

  abstractNote = {Previously, Bloch showed that in a system of interacting nonrelativistic particles the net particle-number current must vanish in any equilibrium state. Bloch’s argument does not generalize easily to the energy current. We devise an alternative argument which proves the vanishing of the net energy currents in equilibrium states of lattice systems as well as systems of nonrelativistic particles with finite-range potential interactions. We discuss some applications of these results. Specifically, we show that neither a one-dimensional (1D) lattice system nor a 1D system of nonrelativistic particles with finite-range potential interactions can flow to a conformal field theory with unequal left-moving and right-moving central charges.},

  doi          = {10.1103/PhysRevLett.123.060601},

  journal      = {Physical Review Letters},

  number       = 6,

  volume       = 123,

  place        = {United States},

  year         = {Tue Aug 06 00:00:00 EDT 2019},

  month        = {Tue Aug 06 00:00:00 EDT 2019}

}

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https://doi.org/10.1103/PhysRevLett.123.060601

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Works referenced in this record:

Energy-Flux Operator for a Lattice
journal, October 1963

Hardy, Robert J.
Physical Review, Vol. 132, Issue 1
DOI: 10.1103/PhysRev.132.168

Conformal invariance, the central charge, and universal finite-size amplitudes at criticality
journal, February 1986

Blöte, H. W. J.; Cardy, John L.; Nightingale, M. P.
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journal, January 2006

Kitaev, Alexei
Annals of Physics, Vol. 321, Issue 1
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Non-Equilibrium Steady States in Conformal Field Theory
journal, January 2014

Bernard, Denis; Doyon, Benjamin
Annales Henri Poincaré, Vol. 16, Issue 1
DOI: 10.1007/s00023-014-0314-8

Many-Particle Physics
book, January 2000

Mahan, Gerald D.
Physics of Solids and Liquids (PSLI)
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Universal term in the free energy at a critical point and the conformal anomaly
journal, February 1986

Affleck, Ian
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The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics
journal, June 1950

Irving, J. H.; Kirkwood, John G.
The Journal of Chemical Physics, Vol. 18, Issue 6
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Note on a Theorem of Bloch Concerning Possible Causes of Superconductivity
journal, February 1949

Bohm, D.
Physical Review, Vol. 75, Issue 3
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Energy Magnetization and the Thermal Hall Effect
journal, November 2011

Qin, Tao; Niu, Qian; Shi, Junren
Physical Review Letters, Vol. 107, Issue 23
DOI: 10.1103/PhysRevLett.107.236601

Works referencing / citing this record:

A Proof of the Bloch Theorem for Lattice Models
journal, September 2019

Watanabe, Haruki
Journal of Statistical Physics, Vol. 177, Issue 4
DOI: 10.1007/s10955-019-02386-1

Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems
text, January 2019

Kapustin, Anton; Spodyneiko, Lev
arXiv
DOI: 10.48550/arxiv.1905.06488

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Title: Absence of Energy Currents in an Equilibrium State and Chiral Anomalies

Abstract

Citation Formats

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Conformal invariance, the central charge, and universal finite-size amplitudes at criticality
journal, February 1986

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

Non-Equilibrium Steady States in Conformal Field Theory
journal, January 2014

Many-Particle Physics
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Universal term in the free energy at a critical point and the conformal anomaly
journal, February 1986

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Note on a Theorem of Bloch Concerning Possible Causes of Superconductivity
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