Signatures of many-body localization in steady states of open quantum systems

Many-body localization (MBL) is a result of the balance between interference-based Anderson localization and many-body interactions in a high-dimensional Fock space. It is expected that dissipation is blurring interference and destroying that balance so that the asymptotic state of a system with an MBL Hamiltonian does not bear localization signatures. This is evidently true in the case of local dephasing which drives any system into an infinite-temperature state. We demonstrate, by using a set of dissipative operators, where each one is acting nontrivially on a pair of neighboring sites (or spins), that an MBL system can be brought into a Hamiltonian-specific steady state. The difference between ergodic and MBL Hamiltonians can be seen in statistics of imbalance, entanglement entropy, and level spacing of the steady-state density operator. By introducing pairwise dissipative operators into an MBL system already exposed to dephasing, these localization signatures can be restored.