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

Abstract

Here, 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 $$\hat{G}$$ in an arbitrary dimension. The classification is described as a function of the real representation theory of $$\hat{G}$$ 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. Finally, 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.

Authors:
ORCiD logo [1];  [1]; ORCiD logo [1];  [1]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States)
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
OSTI Identifier:
1597474
Grant/Contract Number:  
SC0011632; PHY-1607611
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 100; Journal Issue: 19; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Symmetry protected topological states; Band structure methods; Symmetries in condensed matter

Citation Formats

Chen, Yu-An, Kapustin, Anton, Turzillo, Alex, and You, Minyoung. Free and interacting short-range entangled phases of fermions: Beyond the tenfold way. United States: N. p., 2019. Web. doi:10.1103/PhysRevB.100.195128.
Chen, Yu-An, Kapustin, Anton, Turzillo, Alex, & You, Minyoung. Free and interacting short-range entangled phases of fermions: Beyond the tenfold way. United States. doi:https://doi.org/10.1103/PhysRevB.100.195128
Chen, Yu-An, Kapustin, Anton, Turzillo, Alex, and You, Minyoung. Mon . "Free and interacting short-range entangled phases of fermions: Beyond the tenfold way". United States. doi:https://doi.org/10.1103/PhysRevB.100.195128. https://www.osti.gov/servlets/purl/1597474.
@article{osti_1597474,
title = {Free and interacting short-range entangled phases of fermions: Beyond the tenfold way},
author = {Chen, Yu-An and Kapustin, Anton and Turzillo, Alex and You, Minyoung},
abstractNote = {Here, 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 $\hat{G}$ in an arbitrary dimension. The classification is described as a function of the real representation theory of $\hat{G}$ 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. Finally, 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.},
doi = {10.1103/PhysRevB.100.195128},
journal = {Physical Review B},
number = 19,
volume = 100,
place = {United States},
year = {2019},
month = {11}
}

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