Study of anyon condensation and topological phase transitions from a Z_4 topological phase using the projected entangled pair states approach

摘要

We use projected entangled pair states (PEPS) to study topological quantum phase transitions. The local description of topological order in the PEPS formalism allows us to set up order parameters which measure condensation and deconfinement of anyons and serve as substitutes for conventional order parameters. We apply these order parameters, together with anyon-anyon correlation functions and some further probes, to characterize topological phases and phase transitions within a family of models based on a Z_4 symmetry, which contains Z_4 quantum double, toric code, double semion, and trivial phases. We find a diverse phase diagram which exhibits a variety of different phase transitions of both first and second order which we comprehensively characterize, including direct transitions between the toric code and the double semion phase.