Topological Order and Quantum Criticality

TL;DR

This paper explores quantum critical behavior at phase transitions between topological and ordered phases, focusing on deformed toric code models and their associated universality classes, entanglement, and conformal invariance.

Contribution

It introduces specific deformations of the toric code model that exhibit novel quantum critical points, including Lorentz-invariant and conformal transitions, and analyzes their physical properties.

Findings

Identification of Lorentz-invariant quantum critical point in 3D Ising class

Discovery of conformal quantum critical point with 2D Ising correlations

Analysis of entanglement entropy and non-local operators at criticality

Abstract

In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely certain deformations of the toric code model, that exhibit continuous quantum phase transitions. One such deformation leads to a Lorentz-invariant transition in the 3D Ising universality class. An alternative deformation gives rise to a so-called conformal quantum critical point where equal-time correlations become conformally invariant and can be related to those of the 2D Ising model. We study the behavior of several physical observables, such as non-local operators and entanglement entropies, that can be used to characterize these quantum phase transitions. Finally, we briefly consider the role of thermal fluctuations and related phase transitions, before closing with a short overview of field theoretical descriptions of these quantum critical points.