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

Journal Article · 30 January 2020 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.101.045137 · OSTI ID:1762782

Kapustin, Anton ^[1];

^[2]

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

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.

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

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

Grant/Contract Number:: SC0011632

OSTI ID:: 1762782

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 4 Vol. 101; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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