Global Anomaly Detection in Two-Dimensional Symmetry-Protected Topological Phases

Physical Review Letters
Nick BultinckF Verstraete

Abstract

Edge theories of symmetry-protected topological phases are well known to possess global symmetry anomalies. In this Letter we focus on two-dimensional bosonic phases protected by an on-site symmetry and analyze the corresponding edge anomalies in more detail. Physical interpretations of the anomaly in terms of an obstruction to orbifolding and constructing symmetry-preserving boundaries are connected to the cohomology classification of symmetry-protected phases in two dimensions. Using the tensor network and matrix product state formalism we numerically illustrate our arguments and discuss computational detection schemes to identify symmetry-protected order in a ground state wave function.

References

Feb 17, 1986·Physical Review Letters·H W BlöteM P Nightingale
Aug 8, 2009·Physical Review Letters·Frank PollmannJoel E Moore
Jun 28, 2014·Physical Review Letters·Anton Kapustin, Ryan Thorngren
Jul 6, 2014·Physical Review Letters·Yi-Zhuang YouCenke Xu
Jan 28, 2017·Physical Review Letters·Shunsuke C Furuya, Masaki Oshikawa

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Citations

Nov 10, 2018·Physical Review Letters·Robijn VanhoveFrank Verstraete

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