CaltechAUTHORS
  A Caltech Library Service

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

Kapustin, Anton and Spodyneiko, Lev (2019) Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190617-151316187

[img] PDF - Submitted Version
See Usage Policy.

309Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20190617-151316187

Abstract

We show that derivatives of thermal Hall conductance of a 2d lattice quantum system with respect to parameters of the Hamiltonian are well-defined bulk quantities provided correlators of local observables are short-range. This is despite the fact that thermal Hall conductance itself has no meaning as a bulk transport coefficient. We use this to define a relative topological invariant for gapped 2d lattice quantum 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 bulk-boundary correspondence for the chiral central charge. We also show that for Local Commuting Projector Hamiltonians relative thermal Hall conductance vanishes identically, while for free fermionic systems it is related to the electric Hall conductance via the Wiedemann-Franz law.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1905.06488arXivDiscussion Paper
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
Group:Caltech Theory
Record Number:CaltechAUTHORS:20190617-151316187
Persistent URL:http://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:17 Jun 2019 22:31

Repository Staff Only: item control page