Constrained thermalization and topological superconductivity

We examine the thermalization/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 noninteracting limit where topological superconductivity survives together with a significant violation of the eigenstate-thermalization hypothesis (ETH) at finite energy densities. We further identify that the coexistence regime features an anomalous behavior of the von Neumann entanglement entropy as a function of disorder strength, which we attribute to competing ETH violation mechanisms. At low disorder, prethermalization like effects that occur due to lack of hybridization between high-energy eigenstates reflect an approximate particle conservation law. In this regime the system tends to thermalize to a generalized Gibbs (as opposed to a 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 behavior is cut off by strong disorder which obstructs many-body effects thus violating ETH and reducing the entanglement entropy.