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

Kapustin, Anton and Spodyneiko, Lev (2020) Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems. Physical Review B, 101 (4). Art. No. 045137. ISSN 2469-9950. https://resolver.caltech.edu/CaltechAUTHORS:20190617-151316187

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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. 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevB.101.045137DOIArticle
https://arxiv.org/abs/1905.06488arXivDiscussion Paper
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
Spodyneiko, Lev0000-0002-6099-7717
Additional Information:© 2020 American Physical Society. Received 9 October 2019; revised manuscript received 14 January 2020; published 31 January 2020. We thank Y.-A. Chen for participation in the early stages of this work and M. Hastings, H. Watanabe, A. Kitaev, and H. Edelsbrunner for discussions. This research was supported in part by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. A.K. was also supported by the Simons Investigator Award.
Group:Caltech Theory
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Issue or Number:4
Record Number:CaltechAUTHORS:20190617-151316187
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190617-151316187
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96481
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:17 Jun 2019 22:31
Last Modified:31 Jan 2020 20:52

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