Constrained thermalization and topological superconductivity

Abstract

We examine the thermalisation/localization trade off in an interacting and disordered Kitaev model, specifically addressing whether signatures of many-body localization can coexist with the systems topological phase. Using methods applicable to finite size systems, (e.g. the generalized one-particle density matrix, eigenstate entanglement entropy, inverse zero modes coherence length) we identify a regime of parameter space in the vicinity of the non-interacting limit where topological superconductivity survives together with a significant violation of Eigenstate-Thermalisation-Hypothesis (ETH) at finite energy-densities. We further identify an anomalous behaviour of the von Neumann entanglement entropy which can be attributed to the prethermalisation-like effects that occur due to lack of hybridization between high-energy eigenstates reflecting an approximate particle conservation law. In this regime the system tends to thermalise to a generalised Gibbs ensemble (as opposed to the grand canonical ensemble). Moderate disorder tends to drive the system towards stronger hybridization and a standard thermal ensemble, where the approximate conservation law is violated. This behaviour is cutoff by strong disorder which obstructs many body effects thus violating ETH and reducing the entanglement entropy.