Nonequilibrium stationary states of quantum non-Hermitian lattice models

While the band theory of non-Hermitian Hamiltonians and the dynamics they generate have received considerable recent interest, the quantum steady states of such models remain largely unexplored. Here, the authors systematically characterize such states for fermions and bosons using an open quantum system approach. Surprisingly, these steady states exhibit features that cannot be extracted readily from the non-Hermitian Hamiltonian. This includes a macroscopic length scale which characterizes the steady-state occupation but differs from the localization length of the eigenvectors.