Tensor-network approach to phase transitions in string-net models

Sep 13, 2019
8 pages
Published in:
  • Phys.Rev.B 100 (2019) 24, 245125
  • Published: Dec 16, 2019
e-Print:
DOI:

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Abstract: (APS)
We use a recently proposed class of tensor-network states to study phase transitions in string-net models. These states encode the genuine features of the string-net condensate such as, e.g., a nontrivial perimeter law for Wilson loops expectation values, and a natural order parameter detecting the breakdown of the topological phase. In the presence of a string tension, a quantum phase transition occurs between the topological phase and a trivial phase. We benchmark our approach for Z2 string nets and capture the second-order phase transition which is well known from the exact mapping onto the transverse-field Ising model. More interestingly, for Fibonacci string nets, we obtain first-order transitions in contrast with previous studies but in qualitative agreement with mean-field results.
Note:
  • 10 pages, 3 figures
  • Electronic structure and strongly correlated systems