Entanglement and spectra in topological many-body localized phases

Many-body localized systems in which interactions and disorder come together defy the expectations of quantum statistical mechanics: In contrast to ergodic systems, they do not thermalize when undergoing non-equilibrium dynamics. What is less clear, however, is how topological features interplay with many-body localized phases as well as the nature of the transition between a topological and a trivial state within the latter. In this work, we numerically address these questions, using a combination of extensive tensor network calculations, specifically DMRG-X, as well as exact diagonalization, leading to a comprehensive characterization of Hamiltonian spectra and eigenstate entanglement properties. We advocate that the scaling properties of entanglement features characterize many-body localized systems both in topological and trivial situations, but that no longer the entanglement entropy, but mixed-state entanglement measures such as the negativity - a concept inherited from quantum information - can meaningfully be made use of, due to the close to degenerate energy levels.