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Higher-dimensional generalizations of the Berry curvature

Kapustin, Anton and Spodyneiko, Lev (2020) Higher-dimensional generalizations of the Berry curvature. Physical Review B, 101 (23). Art. No. 235130. ISSN 2469-9950. https://resolver.caltech.edu/CaltechAUTHORS:20200303-084023611

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Abstract

A family of finite-dimensional quantum systems with a nondegenerate ground state gives rise to a closed two-form on the parameter space, the curvature of the Berry connection. Its integral over a surface detects the presence of degeneracy points inside the volume enclosed by the surface. We seek generalizations of the Berry curvature to gapped many-body systems in D spatial dimensions which can detect gapless or degenerate points in the phase diagram of a system. Field theory predicts that in spatial dimension D the analog of the Berry curvature is a closed (D+2)-form on the parameter space (the Wess-Zumino-Witten form). We construct such closed forms for arbitrary families of gapped interacting lattice systems in all dimensions. We show that whenever the integral of the Wess-Zumino-Witten form over a (D+2)-dimensional surface in the parameter space is nonzero, there must be gapless edge modes for at least one value of the parameters. These edge modes arise even when the bulk system is in a trivial phase for all values of the parameters and are protected by the nontrivial topology of the phase diagram.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevB.101.235130DOIArticle
https://arxiv.org/abs/2001.03454arXivDiscussion Paper
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
Spodyneiko, Lev0000-0002-6099-7717
Additional Information:© 2020 American Physical Society. Received 20 February 2020; accepted 14 May 2020; published 11 June 2020. A.K. would like to thank D. Freed, M. Freedman, M. Hopkins, A. Kitaev. G. Moore, and C. Teleman for discussions of family invariants of gapped systems and related issues, and P.-S. Hsin and R. Thorngren for collaboration on a related project. We are especially grateful to A. Kitaev for reading a preliminary draft of the paper and pointing out an error. 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.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Issue or Number:23
Record Number:CaltechAUTHORS:20200303-084023611
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200303-084023611
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101674
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:03 Mar 2020 18:38
Last Modified:12 Jun 2020 17:22

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