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Free and interacting short-range entangled phases of fermions: Beyond the tenfold way

Chen, Yu-An and Kapustin, Anton and Turzillo, Alex and You, Minyoung (2019) Free and interacting short-range entangled phases of fermions: Beyond the tenfold way. Physical Review B, 100 (19). Art. No. 195128. ISSN 2469-9950. https://resolver.caltech.edu/CaltechAUTHORS:20181105-095310279

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Abstract

We extend the periodic table of phases of free fermions in the tenfold way symmetry classes to a classification of free fermionic phases protected by an arbitrary on-site unitary symmetry G in an arbitrary dimension. The classification is described as a function of the real representation theory of G and the data of the original periodic table. We also systematically study in low dimensions the relationship between the free invariants and the invariants of short-range entangled interacting phases of fermions. Namely we determine whether a given symmetry protected phase of free fermions is destabilized by sufficiently strong interactions or it remains stable even in the presence of interactions. We also determine which interacting fermionic phases cannot be realized by free fermions. Examples of both destabilized free phases and intrinsically interacting phases are common in all dimensions.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevB.100.195128DOIArticle
https://arxiv.org/abs/1809.04958arXivDiscussion Paper
ORCID:
AuthorORCID
Chen, Yu-An0000-0002-8810-9355
Kapustin, Anton0000-0003-3903-5158
Turzillo, Alex0000-0003-4293-4293
Alternate Title:Free and Interacting Short-Range Entangled Phases of Fermions: Beyond the Ten-Fold Way
Additional Information:© 2019 American Physical Society. Received 3 September 2019; revised manuscript received 3 November 2019; published 18 November 2019. A.T. is grateful to N. Strickland, M. Grant, and M. Wendt for their answers to the MathOverflow question Ref. [23]. This research was supported in part by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. The work of A.K. was partly performed at the Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-1607611. A.K. was also supported by the Simons Investigator Award.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
NSFPHY-1607611
Simons FoundationUNSPECIFIED
Issue or Number:19
Record Number:CaltechAUTHORS:20181105-095310279
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181105-095310279
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90635
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 Nov 2018 17:31
Last Modified:18 Nov 2019 17:57

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