Recently quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. Quantum magnets provide a perfect playground for studying these phase transitions since they can be triggered by many control parameters such as frustration, lattice dimerization, and magnetic field. Most previous studies have focused on the magnetic properties in pure systems. In these systems, responses to the triggering parameters are found to be uniform, leading to homogeneous phases. However little progress has been made so far on the phase transitions and properties in disordered quantum magnets because they are more complicated systems, and few theoretical tools can be applied.
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
Z2 monopole-instantons in the emergent non-Abelian gauge field are key to understanding spontaneous symmetry breaking in the ordered phase.