Continuous transition between Ising magnetic order and a chiral spin liquid

TL;DR

This paper demonstrates a continuous quantum phase transition between a topologically ordered chiral spin liquid and a magnetically ordered phase in 2D Ising spin systems, using effective field theory with Majorana fermions and non-Abelian gauge fields.

Contribution

It introduces a theoretical framework describing a protected continuous transition between topological order and magnetic order in 2D Ising systems, highlighting the role of Majorana zero modes and non-Abelian gauge fields.

Findings

A direct quantum phase transition can occur between chiral spin liquid and magnetic order.

The transition is described by massless Majorana fields coupled to non-Abelian gauge fields.

Majorana zero modes are crucial for understanding symmetry breaking in the ordered phase.

Abstract

The competition between fractionalized spin-liquid states and magnetically ordered phases is an important paradigm in frustrated magnetism. Spin-orbit coupled Mott insulators with Ising-like magnetic anisotropies, such as Kitaev materials, are a particularly rich playground to explore this competition. In this work, we use effective field theory methods to show that a direct quantum phase transition can occur in two-dimensional (2D) Ising spin systems between a topologically ordered chiral spin liquid and a phase with magnetic long-range order. Such a transition can be protected by lattice symmetries and is described by a theory of massless Majorana fields coupled to non-Abelian $SO(N)$ gauge fields with a Chern-Simons term. We further show that Euclidean Majorana zero modes bound to $\mathbb{Z}_2$ monopole-instantons in the emergent non-Abelian gauge field are key to understanding spontaneous symmetry breaking in the ordered phase.