Numerical study of a transition between Z2 topologically ordered phases

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Colleges, School and Institutes


Distinguishing different topologically ordered phases and characterizing phase transitions between them is a difficult task due to the absence of local order parameters. In this paper, we use a combination of analytical and numerical approaches to distinguish two such phases and characterize a phase transition between them. The "toric code" and "double semion" models are simple lattice models exhibiting Z2 topological order. Although both models express the same topological ground state degeneracies and entanglement entropies, they are distinct phases of matter because their emergent quasiparticles obey different statistics. For a 1D model, we tune a phase transition between these two phases and obtain an exact solution to the entire phase diagram, finding a second-order Ising×Ising transition. We then use exact diagonalization to study the 2D case and find indications of a first-order transition. We show that the quasiparticle statistics provides a robust indicator of the distinct topological orders throughout the whole phase diagram.


Original languageEnglish
Article number035117
Pages (from-to)1-9
Number of pages9
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number3
Publication statusPublished - 14 Jul 2014