Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume -, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2013/10/P10024
Keywords
spin chains; ladders and planes (theory); electrical and magnetic phenomena (theory)
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Funding
- German Research Council (DFG) through M Zirnbauer's Leibniz Prize DFG [ZI 513/2-1]
- DFG
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We classify the gapped phases of Z(N) parafermions in one dimension and construct a representative of each phase. Even in the absence of additional symmetries besides parafermionic parity, parafermions may be realized in a variety of phases, one for each divisor n of N. The phases can be characterized by spontaneous symmetry breaking, topology, or a mixture of the two. Purely topological phases arise if n is a unitary divisor, i.e. if n and N/n are co-prime. Our analysis is based on the explicit realization of all symmetry broken gapped phases in the dual Z(N)-invariant quantum spin chains.
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