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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. Physical Review B, 102 (24). Art. No. 245113. ISSN 2469-9950. doi:10.1103/PhysRevB.102.245113.

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We study aspects of the Berry phase in gapped many-body quantum systems by means of effective field theory. Once the parameters are promoted to space-time-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 [C. Cordova, D. S. Freed, H. T. Lam, and N. Seiberg, SciPost Phys. 8, 001 (2020) and SciPost Phys. 8, 002 (2020)]. 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:Article
Related URLs:
URLURL TypeDescription Paper
Kapustin, Anton0000-0003-3903-5158
Thorngren, Ryan0000-0001-9433-3399
Additional Information:© 2020 American Physical Society. Received 6 July 2020; accepted 11 November 2020; published 9 December 2020. We thank Dominic Else, Tobias Holder, Raquel Queiroz, Nathan Seiberg, Ruben Verresen, and Adar Sharon 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 No. DE-SC0011632, and by the Simons Foundation through the Simons Investigator Award.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Issue or Number:24
Record Number:CaltechAUTHORS:20200609-073406092
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103783
Deposited By: Tony Diaz
Deposited On:09 Jun 2020 18:05
Last Modified:16 Nov 2021 18:25

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