The emergence of topological order is one of the most intriguing
phenomena in quantum many-body physics and one of possibly far
reaching relevance -- topological quantum matter is increasingly
appreciated as possible medium for quantum computation purposes.
In this talk, I will discuss the stability of topological quantum
matter when considering the effects of interactions and disorder
on the collective quantum state formed by a set of topological
excitations, so-called anyons. In particular, I will discuss the
formation of a thermal metal of Majorana fermions in a
two-dimensional system of interacting non-Abelian anyons in the
presence of moderate disorder. This bulk metallic phase occurs
for various proposed systems supporting Majorana fermion zero
modes when disorder induces the random pinning of a finite density
of vortices. This includes all two-dimensional topological
superconductors in so-called symmetry class D. A distinct
experimental signature of the thermal metal phase is the presence
of bulk heat transport down to zero temperature. I will finish by
discussing implications for topological quantum computing proposals.