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Frustrated topological symmetry breaking: Geometrical frustration and anyon condensation

2016; American Physical Society; Volume: 94; Issue: 16 Linguagem: Inglês

10.1103/physrevb.94.165110

2469-9977

Marc Daniel Schulz, F. J. Burnell,

Advanced Condensed Matter Physics

We study the phase diagram of a topological string-net-type lattice model in the presence of geometrically frustrated interactions. These interactions drive several phase transitions that reduce the topological order, leading to a rich phase diagram including both Abelian $({\mathbb{Z}}_{2})$ and non-Abelian $(\text{Ising}\ifmmode\times\else\texttimes\fi{}\overline{\text{Ising}})$ topologically ordered phases, as well as phases with broken translational symmetry. Interestingly, one of these phases simultaneously exhibits (Abelian) topological order and long-ranged order due to translational symmetry breaking, with nontrivial interactions between excitations in the topological order and defects in the long-ranged order. We introduce a variety of effective models, valid along certain lines in the phase diagram, which can be used to characterize both topological and symmetry-breaking order in these phases and in many cases allow us to characterize the phase transitions that separate them. We use exact diagonalization and high-order series expansion to study areas of the phase diagram where these models break down and to approximate the location of the phase boundaries.