Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems

Kapustin, Anton; Spodyneiko, Lev

doi:10.1103/physrevb.101.045137

Title: Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems

Abstract

We derive a Kubo-like formula for the thermal Hall conductance of a 2d lattice systems which is free from ambiguities associated with the definition of energy magnetization. We use it to define a relative topological invariant of gapped 2d lattice systems at zero temperature. Up to a numerical factor, it can be identified with the difference of chiral central charges for the corresponding edge modes. This establishes the bulk-boundary correspondence for the chiral central charge. Here, we also show that for any local commuting projector Hamiltonian, the relative chiral central charge vanishes, while for free fermionic systems, it is related to the zero-temperature electric Hall conductance via the Wiedemann-Franz law.

Authors:

Kapustin, Anton ^[1];

^[1]

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

Publication Date:: Fri Jan 31 00:00:00 EST 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:: 1762782

Grant/Contract Number:: SC0011632

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. B

Additional Journal Information:: Journal Volume: 101; Journal Issue: 4; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Edge states; Quantum phase transitions; Thermal Hall effect; Topological phases of matter; Transport phenomena

Citation Formats


                    Kapustin, Anton, and Spodyneiko, Lev. Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems.  United States: N. p., 2020. 
Web.  doi:10.1103/physrevb.101.045137.

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                    Kapustin, Anton, & Spodyneiko, Lev. Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems.  United States.  https://doi.org/10.1103/physrevb.101.045137

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                    Kapustin, Anton, and Spodyneiko, Lev. Fri .  
"Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems".  United States.  https://doi.org/10.1103/physrevb.101.045137.  https://www.osti.gov/servlets/purl/1762782.

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@article{osti_1762782,

  title        = {Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems},

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

  abstractNote = {We derive a Kubo-like formula for the thermal Hall conductance of a 2d lattice systems which is free from ambiguities associated with the definition of energy magnetization. We use it to define a relative topological invariant of gapped 2d lattice systems at zero temperature. Up to a numerical factor, it can be identified with the difference of chiral central charges for the corresponding edge modes. This establishes the bulk-boundary correspondence for the chiral central charge. Here, we also show that for any local commuting projector Hamiltonian, the relative chiral central charge vanishes, while for free fermionic systems, it is related to the zero-temperature electric Hall conductance via the Wiedemann-Franz law.},

  doi          = {10.1103/physrevb.101.045137},

  journal      = {Physical Review. B},

  number       = 4,

  volume       = 101,

  place        = {United States},

  year         = {Fri Jan 31 00:00:00 EST 2020},

  month        = {Fri Jan 31 00:00:00 EST 2020}

}

Copy to clipboard

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Works referencing / citing this record:

Resonant thermal Hall effect of phonons coupled to dynamical defects
journal, November 2022

Guo, Haoyu; Joshi, Darshan G.; Sachdev, Subir
Proceedings of the National Academy of Sciences, Vol. 119, Issue 46
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Title: Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems

Abstract

Citation Formats

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Absence of energy currents in an equilibrium state and chiral anomalies text, January 2019

Topological field theory and thermal responses of interacting topological superconductors journal, July 2011

Quantized thermal transport in the fractional quantum Hall effect journal, June 1997

Thermoelectric Response of an Interacting Two-Dimensional Electron Gas in Quantizing Magnetic Field text, January 1996

Gravitational Anomalies and Thermal Hall effect in Topological Insulators text, January 2012

Cross-Correlated Responses of Topological Superconductors and Superfluids journal, January 2012

Hydrodynamics on the lowest Landau level journal, June 2015

Hydrodynamics on the lowest Landau level preprint, January 2014

Insensitivity of bulk properties to the twisted boundary condition journal, October 2018

Energy Magnetization and the Thermal Hall Effect journal, November 2011

Energy Magnetization and Thermal Hall Effect text, January 2011

String-net condensation: A physical mechanism for topological phases journal, January 2005

Anyons in an exactly solved model and beyond text, January 2005

Linear response theory and the KMS condition journal, February 1975

Phonon-glass-like behavior of magnetic origin in single-crystal Tb 2 Ti 2 O 7 journal, June 2013

Local Commuting Projector Hamiltonians and the Quantum Hall Effect journal, May 2019

Giant thermal Hall conductivity in the pseudogap phase of cuprate superconductors journal, July 2019

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

Theory of Thermal Transport Coefficients journal, September 1964

Note on a Theorem of Bloch Concerning Possible Causes of Superconductivity journal, February 1949

Gravitational anomalies and thermal Hall effect in topological insulators journal, May 2012

On Onsager's Principle of Microscopic Reversibility journal, April 1945

Many-Particle Physics book, January 2000

Observation of half-integer thermal Hall conductance journal, June 2018

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

Resonant thermal Hall effect of phonons coupled to dynamical defects journal, November 2022

String-net condensation: A physical mechanism for topological phases
text, January 2004

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

Topological field theory and thermal responses of interacting topological superconductors
text, January 2010

Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
journal, January 2012

Absence of Energy Currents in an Equilibrium State and Chiral Anomalies
journal, August 2019

Insensitivity of bulk properties to the twisted boundary condition
text, January 2018

Many-Particle Physics
journal, March 1982

Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
text, January 2010

Cross-Correlated Responses of Topological Superconductors and Superfluids
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Low-energy effective theory in the bulk for transport in a topological phase
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Absence of energy currents in an equilibrium state and chiral anomalies
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Topological field theory and thermal responses of interacting topological superconductors
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Quantized thermal transport in the fractional quantum Hall effect
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Thermoelectric Response of an Interacting Two-Dimensional Electron Gas in Quantizing Magnetic Field
text, January 1996

Gravitational Anomalies and Thermal Hall effect in Topological Insulators
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Cross-Correlated Responses of Topological Superconductors and Superfluids
journal, January 2012

Hydrodynamics on the lowest Landau level
journal, June 2015

Hydrodynamics on the lowest Landau level
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Insensitivity of bulk properties to the twisted boundary condition
journal, October 2018

Energy Magnetization and the Thermal Hall Effect
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Energy Magnetization and Thermal Hall Effect
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String-net condensation: A physical mechanism for topological phases
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Anyons in an exactly solved model and beyond
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Phonon-glass-like behavior of magnetic origin in single-crystal Tb $_{2}$ Ti $_{2}$ O $_{7}$
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