Time reversal invariant gapped boundaries of the double semion state

Fiona Burnell, Xie Chen, Alexei Kitaev, Max Metlitski, Ashvin Vishwanath

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4 Scopus citations

Abstract

The boundary of a fractionalized topological phase can be gapped by condensing a proper set of bosonic quasiparticles. Interestingly, in the presence of a global symmetry, such a boundary can have different symmetry transformation properties. Here we present an explicit example of this kind, in the double semion state with time reversal symmetry. We find two distinct cases where the semionic excitations on the boundary can transform either as time reversal singlets or as time reversal (Kramers) doublets, depending on the coherent phase factor of the Bose condensate. The existence of these two possibilities are demonstrated using both field-theory argument and exactly solvable lattice models. Furthermore, we study the domain walls between these two types of gapped boundaries and find that the application of time reversal symmetry tunnels a semion between them.

Original languageEnglish (US)
Article number235161
JournalPhysical Review B
Volume93
Issue number23
DOIs
StatePublished - Jun 30 2016

Bibliographical note

Funding Information:
We would like to thank Lukasz Fidkowski, Zhenghan Wang, Meng Cheng, and T. Senthil for discussion. X.C. is supported by the Miller Institute for Basic Research in Science at UC Berkeley, the Caltech Institute for Quantum Information and Matter and the Walter Burke Institute for Theoretical Physics. A.V. is supported by the Templeton Foundation. FJB is supported by NSF DMR-1352271 and Sloan FG-2015- 65927.

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