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On topological phases of spin chains | | Kasper Duivenvoorden
; Thomas Quella
; | | Date: |
12 Jun 2012 | | Abstract: | Topological phases of one-dimensional spin systems with various symmetries
have been classified using group cohomology. In this paper, we revisit this
problem for general spin chains which are invariant under a continuous on-site
symmetry group G. We evaluate the relevant cohomology groups and find that the
topological phases are in one-to-one correspondence with the elements of the
fundamental group of G if G is compact, simple and connected. For spin chains
with symmetry PSU(N)=SU(N)/Z_N our analysis implies the existence of N distinct
topological phases. For symmetry groups of orthogonal, symplectic or
exceptional type we find up to four different phases. Our work suggests a
natural generalization of Haldane’s conjecture beyond SU(2). | | Source: | arXiv, 1206.2462 | | Services: | Forum | Review | PDF | Favorites | |
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