Study of anyon condensation and topological phase transitions from a $\mathbb{Z}_4$ topological phase using Projected Entangled Pair States

摘要

We use Projected Entangled Pair States (PEPS) to study topological quantumphase transitions. The local description of topological order in the PEPSformalism allows us to set up order parameters which measure condensation anddeconfinement of anyons, and serve as a substitute for conventional orderparameters. We apply these order parameters, together with anyon-anyoncorrelation functions and some further probes, to characterize topologicalphases and phase transitions within a family of models based on a $\mathbb Z_4$symmetry, which contains $\mathbb Z_4$ quantum double, toric code, doublesemion, and trivial phases. We find a diverse phase diagram which exhibits avariety of different phase transitions of both first and second order which wecomprehensively characterize, including direct transitions between the toriccode and the double semion phase.