Chiral metals and entrapped insulators in a one-dimensional topological non-Hermitian system

In this work we study many-body 'steady states' that arise in the non-Hermitian generalisation of the non-interacting Su-Schrieffer-Heeger model at a finite density of fermions. We find that the hitherto known phase diagrams for this system, derived from the single-particle gap closings, in fact correspond to distinct non-equilibrium phases, which either carry finite currents or are dynamical insulators where particles are entrapped. Each of these have distinct quasi-particle excitations and steady state correlations and entanglement properties. Looking at finite-sized systems, we further modulate the boundary to uncover the topological features in such steady states -- in particular the emergence of leaky boundary modes. Using a variety of analytical and numerical methods we develop a theoretical understanding of the various phases and their transitions, and uncover the rich interplay of non-equilibrium many-body physics, quantum entanglement and topology in a simple looking, yet a rich model system.