Quantum phase transition in the $Z_3$ Kitaev-Potts model

TL;DR

This paper investigates the stability of the topological order in the $Z_3$ Kitaev model when coupled with the Potts model, revealing a first-order phase transition that breaks topological order.

Contribution

It introduces a detailed analysis of the phase transition in the $Z_3$ Kitaev-Potts model using series expansions and mean-field methods, highlighting the breakdown of topological order.

Findings

Topological phase breaks down via a first-order transition.

Ground state energy and quasiparticle gap indicate phase change.

Entanglement measure captures the phase transition.

Abstract

The stability of the topological order phase induced by the $Z_3$ Kitaev model, which is a candidate for fault-tolerant quantum computation, against the local order phase induced by the 3-State Potts model is studied. We show that the low energy sector of the Kitaev-Potts model is mapped to the Potts model in the presence of transverse magnetic field. Our study relies on two high-order series expansion based on continuous unitary transformations in the limits of small- and large-Potts couplings as well as mean-field approximation. Our analysis reveals that the topological phase of the $Z_3$ Kitaev model breaks down to the Potts model through a first order phase transition. We capture the phase transition by analysis of the ground state energy, one-quasiparticle gap and geometric measure of entanglement.