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Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena

Hsin, Po-Shen and Kapustin, Anton and Thorngren, Ryan (2020) Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20200609-073406092

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Abstract

We study aspects of Berry phase in gapped many-body quantum systems by means of effective field theory. Once the parameters are promoted to spacetime-dependent background fields, such adiabatic phases are described by Wess-Zumino-Witten (WZW) and similar terms. In the presence of symmetries, there are also quantized invariants capturing generalized Thouless pumps. Consideration of these terms provides constraints on the phase diagram of many-body systems, implying the existence of gapless points in the phase diagram which are stable for topological reasons. We describe such diabolical points, realized by free fermions and gauge theories in various dimensions, which act as sources of "higher Berry curvature" and are protected by the quantization of the corresponding WZW terms or Thouless pump terms. These are analogous to Weyl nodes in a semimetal band structure. We argue that in the presence of a boundary, there are boundary diabolical points---parameter values where the boundary gap closes---which occupy arcs ending at the bulk diabolical points. Thus the boundary has an "anomaly in the space of couplings" in the sense of Córdova et al. Consideration of the topological effective action for the parameters also provides some new checks on conjectured infrared dualities and deconfined quantum criticality in 2+1d.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2004.10758arXivDiscussion Paper
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
Thorngren, Ryan0000-0001-9433-3399
Additional Information:We thank Dominic Else, Tobias Holder, Raquel Queiroz, Nathan Seiberg, and Ruben Verresen for discussions. A. K. is grateful to Lev Spodyneiko for a collaboration on a closely related project. The work is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number de-sc0011632, and by the Simons Foundation through the Simons Investigator Award.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20200609-073406092
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200609-073406092
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103783
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Jun 2020 18:05
Last Modified:09 Jun 2020 18:05

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