Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
| Autor: | Michael Mulligan, Eugeniu Plamadeala, Chetan Nayak, Meng Cheng, Jennifer Cano, Jon Yard |
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| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Physics
High Energy Physics - Theory Quantum Physics Strongly Correlated Electrons (cond-mat.str-el) Root of unity FOS: Physical sciences Quantum Hall effect Condensed Matter Physics Topology 01 natural sciences Topological entropy in physics Symmetry protected topological order 010305 fluids & plasmas Electronic Optical and Magnetic Materials Condensed Matter - Strongly Correlated Electrons Tensor product High Energy Physics - Theory (hep-th) 0103 physical sciences Topological order Abelian group Quantum Physics (quant-ph) 010306 general physics Topological quantum number |
| Popis: | 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 $\nu=8$ and 12, with experimentally-testable consequences. We show that this can occur in Abelian fractional quantum Hall states as well, with the simplest examples being at $\nu=8/7, 12/11, 8/15, 16/5$. We give a general criterion for the existence of multiple distinct chiral edge phases for the same bulk phase and discuss experimental consequences. Edge phases correspond to lattices while bulk phases correspond to genera of lattices. Since there are typically multiple lattices in a genus, the bulk-edge correspondence is typically one-to-many; there are usually many stable fully chiral edge phases corresponding to the same bulk. We explain these correspondences using the theory of integral quadratic forms. 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 shows that every Abelian topological phase can be decomposed into a tensor product of theories associated with prime numbers $p$ in which every quasiparticle has a topological spin that is a $p^n$-th root of unity for some $n$. It also leads to a simple demonstration that all Abelian topological phases can be represented by $U(1)^N$ Chern-Simons theory parameterized by a K-matrix. Comment: 26 pages, 1 table and 3 appendices; published version |
| Databáze: | OpenAIRE |
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