  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.

Strongly Correlated Electrons;High Energy Physics - Theory