Spectral Properties and Stability of a Two-Chain non-Hermitian Hubbard Model

Non-Hermitian models are known to host exotic features, such as the non-Hermitian skin effect and winding number topology in the complex spectrum, which are absent in their Hermitian counterparts. The Hatano-Nelson model, with its various generalizations, has served as the quintessential model for theoretical studies of such systems and has been experimentally realized in various settings. In spite of such progress, relatively little work has been done to further understand such models beyond the non-interacting regime. In this study, we consider a generalized non-Hermitian Hubbard model within such a paradigm. The model exhibits a transition between a complex and completely real spectrum, for which we provide numerical evidence based on exact diagonalization calculations suggesting the robustness of such behaviour as one approaches the thermodynamic limit. We also find robustness in this transition as one approaches the half-filling sector. However, at the level of full quantum master equation dynamics when one no longer neglects quantum jump terms, the behaviour of these systems beyond a non-Hermitian effective Hamiltonian description can be questioned. Therefore, we also investigate the full dynamics of such systems with the quantum trajectory method.