Gauging anomalous unitary operators

Yuhan Liu, Hassan Shapourian, Paolo Glorioso, and Shinsei Ryu

Phys. Rev. B 104, 155144 – Published 25 October 2021

Abstract

Boundary theories of static bulk topological phases of matter are obstructed in the sense that they cannot be realized on their own as isolated systems. The obstruction can be quantified/characterized by quantum anomalies, in particular when there is a global symmetry. Similarly, topological Floquet evolutions can realize obstructed unitary operators at their boundaries. In this paper, we discuss the characterization of such obstructions by using quantum anomalies. As a particular example, we discuss time-reversal symmetric boundary unitary operators in one and two spatial dimensions, where the anomaly emerges as we gauge the so-called Kubo-Martin-Schwinger (KMS) symmetry. We also discuss mixed anomalies between particle number conserving U(1) symmetry and discrete symmetries, such as $C$ and $CP$ , for unitary operators in odd spatial dimensions that can be realized at the boundaries of topological Floquet systems in even spatial dimensions.

Received 20 April 2021
Revised 6 October 2021
Accepted 12 October 2021

DOI:https://doi.org/10.1103/PhysRevB.104.155144

Physics Subject Headings (PhySH)

Symmetry protected topological states Topological phases of matter

Floquet systems

Effective field theory Gauge theory techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yuhan Liu ^1,2, Hassan Shapourian³, Paolo Glorioso ⁴, and Shinsei Ryu⁵

¹Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA
²James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
³Microsoft Station Q, Santa Barbara, California 93106, USA
⁴Department of Physics, Stanford University, Stanford, California 94305, USA
⁵Department of Physics, Princeton University, Princeton, New Jersey 08540, USA