Entanglement signatures of topological phase transitions in a dirty Weyl semimetal

Abstract

Three-dimensional Weyl semimetals (WSMs) constitute paradigmatic gapless topological phases whose nodal structure is stable against weak perturbations, including disorder. Two distinct ways to destroy the topology of the Weyl nodes are through pairwise annihilation in momentum space or by sufficiently strong disorder that eliminates the quasiparticle pole, driving the system into a non-Fermi-liquid diffusive-metallic state. In this work, we study the evolution of entanglement spectrum and entanglement entropy of a dirty WSM as it undergoes these two topological transitions. In the clean limit, the WSM topology is reflected by a locus of $ξ=1/2$ eigenvalues of the reduced correlation matrix mirroring the structure of Fermi arcs. We show that disorder broadens this feature into a finite-width distribution, which disappears either through a gradual loss of spectral weight upon node annihilation or by melting into the background at the onset of metallicity. When tuning across the disorder-driven transition, the scaling of the Rényi entropies observed for weak disorder gradually breaks down as the system approaches the critical disorder strength.