We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner by constructing an appropriate open quantum system. We focus on the quantum steady states of such models for both fermionic and bosonic systems. Surprisingly, key features and spatial structures in the steady state cannot be simply understood from the non-Hermitian Hamiltonian alone. Using the 1D Hatano-Nelson model as a paradigmatic example, we show that the steady state has a marked sensitivity to boundary conditions. In particular, the open boundary system can exhibit a large macroscopic length scale, despite having no corresponding long timescale. These effects persist in more general models and are distinct from the localization physics associated with the non-Hermitian skin effect. Further, particle statistics play an unexpected role: The steady-state density profile is dramatically different for fermions versus bosons. Our paper highlights the key role of fluctuations in quantum realizations of non-Hermitian dynamics and provides a starting point for future work on engineered steady states of open quantum systems.

• Received 19 March 2021
• Accepted 27 January 2022

DOI:https://doi.org/10.1103/PhysRevB.105.064302