Symmetry-protected topological phases and quantum anomalies

Hsieh, Chang-Tse

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https://hdl.handle.net/2142/98272 Copy

Description

Title

Symmetry-protected topological phases and quantum anomalies

Author(s)

Hsieh, Chang-Tse

Issue Date

2017-07-11

Director of Research (if dissertation) or Advisor (if thesis)

Ryu, Shinsei

Doctoral Committee Chair(s)

Stone, Michael

Committee Member(s)

• Leigh, Robert G.
• Eckstein, James N.

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2017-08

Type of Resource

text

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Copyright and License Information

Copyright 2017 Chang-Tse Hsieh

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