PIRSA:14050011

Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases

Cano, J. (2014). Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases. Perimeter Institute. https://pirsa.org/14050011

Cano, Jennifer. Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases. Perimeter Institute, May. 09, 2014, https://pirsa.org/14050011 

          @misc{ pirsa_PIRSA:14050011,
            doi = {10.48660/14050011},
            url = {https://pirsa.org/14050011},
            author = {Cano, Jennifer},
            keywords = {Condensed Matter},
            language = {en},
            title = {Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {may},
            note = {PIRSA:14050011 see, \url{https://pirsa.org}}
          }

Jennifer Cano University of California, Santa Barbara

Talk numberPIRSA:14050011
DOI10.48660/14050011
Collection
Talk Type Scientific Series
Subject

Abstract

The same bulk two-dimensional topological phase can have multiple distinct, fully-chiral edge phases. We show that this can occur in the integer quantum Hall states at fillings 8 and 12 with experimentally-testable consequences. We also show examples for Abelian fractional quantum Hall states, the simplest examples being at filling fractions 8/7, 12/11, 8/15, 16/5. For all examples, we propose experiments that can distinguish distinct edge phases. Our results are summarized by the observation that edge phases correspond to lattices while bulk phases correspond to genera of lattices. Since there are typically multiple lattices in a genus, there are usually many stable fully chiral edge phases corresponding to the same bulk. We show that fermionic systems can have edge phases with only bosonic low-energy excitations and discuss a fermionic generalization of the relation between bulk topological spins and the central charge. The latter follows from our demonstration that every fermionic topological phase can be represented as a bosonic topological phase, together with some number of filled Landau levels. Our analysis also leads to a simple demonstration that all Abelian topological phases can be represented by a Chern-Simons theory parameterized by a K-matrix.