Free and interacting short-range entangled phases of fermions: Beyond the tenfold way
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.
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.Attached Files
Published - PhysRevB.100.195128.pdf
Submitted - 1809.04958.pdf
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Additional details
- Alternative title
- Free and Interacting Short-Range Entangled Phases of Fermions: Beyond the Ten-Fold Way
- Eprint ID
- 90635
- Resolver ID
- CaltechAUTHORS:20181105-095310279
- DE-SC0011632
- Department of Energy (DOE)
- PHY-1607611
- NSF
- Simons Foundation
- Created
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2018-11-06Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field