A quantum topological phase transition at the microscopic level

TL;DR

This paper investigates a quantum phase transition in an extended toric code model, revealing a topological entropy jump at the critical point while local observables indicate a second-order transition.

Contribution

It provides an exact ground state analysis of a topological phase transition in a spin model extending the toric code, highlighting the behavior of topological entropy.

Findings

Topological entropy remains constant up to the critical point

Topological entropy jumps to zero after the transition

Transition is second order despite the entropy jump

Abstract

We study a quantum phase transition between a phase which is topologically ordered and one which is not. We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling constant that takes the system across the phase transition. We compute the entanglement and the topological entropy of the system as a function of this coupling constant, and show that the topological entropy remains constant all the way up to the critical point, and jumps to zero beyond it. Despite the jump in the topological entropy, the transition is second order as detected via any local observable.