Breakdown of a perturbed Z_N topological phase

TL;DR

This paper investigates the stability of a generalized Z_N topological phase, specifically the Z_3 toric code, under local perturbations, revealing phase transitions and topological multi-critical points.

Contribution

It provides a detailed analysis of phase transitions in the perturbed Z_3 toric code, highlighting the existence of multi-critical points and extending understanding beyond the conventional Z_2 case.

Findings

Identified first- and second-order phase transitions.

Discovered topological multi-critical points.

Applied high-order series expansions and variational techniques.

Abstract

We study the robustness of a generalized Kitaev's toric code with Z_N degrees of freedom in the presence of local perturbations. For N=2, this model reduces to the conventional toric code in a uniform magnetic field. A quantitative analysis is performed for the perturbed Z_3 toric code by applying a combination of high-order series expansions and variational techniques. We provide strong evidences for first- and second-order phase transitions between topologically-ordered and polarized phases. Most interestingly, our results also indicate the existence of topological multi-critical points in the phase diagram.