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Ground-State Degeneracy of Topological Phases on Open Surfaces.
- Source :
-
Physical Review Letters . 2/20/2015, Vol. 114 Issue 7, p076401-1-076401-5. 5p. - Publication Year :
- 2015
-
Abstract
- We relate the ground state degeneracy of a non-Abelian topological phase on a surface with boundaries to the anyon condensates that break the topological phase into a trivial phase. Specifically, we propose that gapped boundary conditions of the surface are in one-to-one correspondence with the sets of condensates, each being able to completely break the phase, and we substantiate this by examples. The ground state degeneracy resulting from a particular boundary condition coincides with the number of confined topological sectors due to the corresponding condensation. These lead to a generalization of the Laughlin- Tao-Wu charge-pumping argument for Abelian fractional quantum Hall states to encompass non-Abelian topological phases, in the sense that an anyon loop of a confined anyon winding a nontrivial cycle can pump a condensed anyon from one boundary to another. Such generalized pumping may find applications in quantum control of anyons, eventually realizing topological quantum computation. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00319007
- Volume :
- 114
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Physical Review Letters
- Publication Type :
- Academic Journal
- Accession number :
- 101470105
- Full Text :
- https://doi.org/10.1103/PhysRevLett.114.076401