Robustness of a perturbed topological phase

TL;DR

This paper studies how a topological phase in the toric code model remains stable or transitions under a uniform magnetic field, revealing a new universality class during the phase transition.

Contribution

It provides a detailed analysis of the phase transition nature and universality classes in the toric code model under magnetic perturbations.

Findings

Topological phase transition occurs at strong magnetic fields.

Transition order depends on magnetic field orientation.

A new topological universality class is identified.

Abstract

We investigate the stability of the topological phase of the toric code model in the presence of a uniform magnetic field by means of variational and high-order series expansion approaches. We find that when this perturbation is strong enough, the system undergoes a topological phase transition whose first- or second-order nature depends on the field orientation. When this transition is of second order, it is in the Ising universality class except for a special line on which the critical exponent driving the closure of the gap varies continuously, unveiling a new topological universality class.