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. doi:10.1103/PhysRevB.101.045137. 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.
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| 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 | |||||||||
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| Issue or Number: | 4 | |||||||||
| DOI: | 10.1103/PhysRevB.101.045137 | |||||||||
| 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: | 16 Nov 2021 17:21 |
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