Disordered Weyl Semimetals: From Lattice Models to the Continuum

We will discuss numerical studies of disordered Weyl semimetals focusing on the effects of rare regions at low energy. We will review our work on lattice models of Weyl semimetals which demonstrates the existence of rare region induced non-perturbative eigenstates, an exponentially small but non-zero density of states at the Weyl node, an exponentially large quasiparticle lifetime, and an avoided quantum critical point. We will then present our recent study of a single Weyl cone in the presence of short-range disorder. To numerically handle the continuum we represent the Hamiltonian in a "mixed" way between real and momentum space so that we are able to invoke fast Fourier transforms to take advantage of efficient numerical routines (such as Lanczos and the kernel polynomial method) that rely on sparse matrix-vector multiplications. As a result, we can reach sufficiently large system sizes that are comparable to our lattice model calculations. We will report results on the nature of rare regions and the density of states as a function of the strength of disorder and the ultra violet cut off, as well as compare and contrast single-node and multi-node results. In all of the cases studied, we will demonstrate that the putative semimetal to diffusive transition is rounded into a cross over.