Many-Body Non-Hermitian Transitions by Controlling Boundary in Hubbard Chain

Non-Hermitian systems exhibit strong energy spectrum sensitivity to boundary conditions and nontrivial topological phases. These systems have recently gained significant interest due to advancements in controlling dissipation and understanding the environment's effect on closed quantum many-body systems. We discuss the effects of tuning boundaries on the localization properties of a one-dimensional non-reciprocal fermionic chain. Using numerical simulations, it has recently been established that many-body localization (MBL) is preserved in Hubbard models with non-reciprocal coupling and dissipation. We reveal the interference of boundary-driven non-Hermitian accumulation of particles dubbed the non-Hermitian skin effect (NHSE) with MBL. A finite boundary parameter results in real-complex spectral transitions with nonreciprocal hopping at weak disorder, while at strong disorder many-body localization washes away spectral transitions, leading to dynamical stability and a real eigenvalue spectrum. The nearest-neighbor level distribution changes from Gaussian orthogonal ensemble (GOE) to Ginibre distribution with boundary parameters corresponding to spectral transitions in weak disorder. As the degree of non-reciprocity reduces, the (biorthogonal) inverse participation ratio approaches zero, signaling the absence of skin-localization in reciprocal systems. The time evolution of local densities demonstrates atomic localizations at the first site, while that of imbalance shows relaxation to a finite value. This confirms NHSE-driven localization with non-reciprocal hopping. The steady imbalance and logarithmic growth of entanglement entropy at strong disorder validate MBL's characteristics in interacting non-Hermitian chain. Our results are timely in view of recent progress in engineering non-reciprocal tunneling via reservoir coupling, thus offering a possibility to realize boundary-driven phase transitions in quantum gas experiments.