Detecting topological orders through continuous quantum phase transition

TL;DR

This paper investigates a novel critical point in a continuous quantum phase transition that breaks Z2 symmetry and involves a change in topological order, providing experimental ways to detect topological phases.

Contribution

It introduces a new critical point beyond the Ising universality class, linking topological order changes with measurable critical exponents.

Findings

Identification of a new critical point not in the Ising class

Proposal to measure critical exponents to detect topological order

Demonstration that topological order changes across the transition

Abstract

We study a continuous quantum phase transition that breaks a $Z_2$ symmetry. We show that the transition is described by a new critical point which does not belong to the Ising universality class, despite the presence of well defined symmetry breaking order parameter. The new critical point arises since the transition not only break the $Z_2$ symmetry, it also changes the topological/quantum order in the two phases across the transition. We show that the new critical point can be identified in experiments by measuring critical exponents. So measuring critical exponents and identifying new critical points is a way to detect new topological phases and a way to measure topological/quantum orders in those phases.