2013/04/29 by Eugeniu Plamadeala, Michael Mulligan, Chetan Nayak · 2 citations
Mathematics · Physics and Astronomy · #Anyon #Boson #Central charge #Charge (physics) #Cold Atom Physics and Bose-Einstein Condensates #Combinatorics #Computer science #Conformal map #Duality (order theory) #Geometry #Integer (computer science) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #Topological quantum computer #Unimodular matrix #Uniqueness #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevb.88.045131
published as Phys. Rev. B 88, 045131 (2013) · 23 pages, 6 figures; reference added, clarification on SRE
arxiv created 2013/04/29 · openalex publication_date 2013/07/26 · arxiv updated 2013/10/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider states of bosons in two dimensions that do not support anyons in the bulk, but nevertheless have stable chiral edge modes that are protected even without any symmetry. Such states must have edge modes with central charge c=8k for integer k. While there is a single such state with c=8, there are, naively, two such states with c=16, corresponding to the two distinct even unimodular lattices in 16 dimensions. However, we show that these two phases are the same in the bulk, which is a consequence of the uniqueness of signature (8k+n,n) even unimodular lattices. The bulk phases are stably equivalent, in a sense that we make precise. However, there are two different phases of the edge corresponding to these two lattices, thereby realizing a novel form of the bulk-edge correspondence. Two distinct fully chiral edge phases are associated with the same bulk phase, which is consistent with the uniqueness of the bulk since the transition between them, which is generically first order, can occur purely at the edge. Our construction is closely related to T duality of toroidally compactified heterotic strings. We discuss generalizations of these results.