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Title:Symmetry-protected topological phases and quantum anomalies
Author(s):Hsieh, Chang-Tse
Director of Research:Ryu, Shinsei
Doctoral Committee Chair(s):Stone, Michael
Doctoral Committee Member(s):Leigh, Robert G.; Eckstein, James N.
Department / Program:Physics
Discipline:Physics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Symmetry-protected topological phases
Topological insulators and superconductors
Classification
Strongly correlated systems
Quantum anomalies
Orientifold conformal field theories
Discrete gauge anomalies
't Hooft anomalies
Abstract:We present the correspondence between symmetry-protected topological (SPT) phases and their anomalous boundary states, based on examples in various spacetime dimensions. Through the study of the effect of interactions on these SPT phases, we discovered a new formalism of quantum anomalies, associated with discrete spacetime (such as time-reversal and spatial reflection) symmetries in particular, to classify distinct interacting topological phases. An example is the Z2 classification of the (2+1)d topological insulator protected by charge U(1) and time-reversal (or CP) symmetries, which can be deduced by the form of the global U(1) gauge anomalies on its edge theories defined on closed unorientable manifolds. In this case, the nontrivial phase (in free systems) is robust against electron interactions. Another example is the (3+1)d topological superconductor protected by only time-reversal or reflection symmetry. For this system, we identified the bulk phase by studying the global gravitational anomalies of the surface theories formulated on unorientable spacetime manifolds, and also discussed its connection to the collapse of the non-interacting classification by an integer Z to Z16, in the presence of interactions. We also revisit the problem of gauging a discrete internal symmetry in theories of chiral (Weyl) fermions in 3+1 dimensions – which have not been fully understood so far – from the perspective of fermionic SPT phases in 4+1 dimensions. Comparing with the previous results, we give a complete answer for the anomalies constraints on the discrete symmetry, as our approach is based on purely geometrical considerations, namely, our assumption is more fundamental and general. Furthermore, our result also provides an understanding of gapped states of fermions with anomalous discrete symmetries, and we present a model, based on weak coupling, for constructing these anomalous gapped states.
Issue Date:2017-07-11
Type:Thesis
URI:http://hdl.handle.net/2142/98272
Rights Information:Copyright 2017 Chang-Tse Hsieh
Date Available in IDEALS:2017-09-29
Date Deposited:2017-08


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