Boundary-driven many-body phase transitions in a non-Hermitian disordered fermionic chain

TL;DR

This paper investigates how boundary conditions influence phase transitions in a disordered, non-Hermitian fermionic chain, revealing boundary-driven spectral changes, localization effects, and dynamic behaviors in many-body systems.

Contribution

It uncovers the interplay between boundary sensitivity, disorder, and non-reciprocal hopping in many-body non-Hermitian systems, highlighting real-complex spectral transitions and localization phenomena.

Findings

Boundary parameter induces real-complex spectral transitions at weak disorder.

Strong disorder leads to many-body localization and spectral stability.

Boundary sensitivity affects level statistics, participation ratios, and quench dynamics.

Abstract

The non-Hermitian systems exhibit extreme sensitivity to the boundary conditions. The change in the eigenspectrum with tunning boundary parameter is intimately connected to the non-Hermitian skin effect. The single-particle systems are affected by the boundary perturbations; however the interplay of a random disorder potential and non-reciprocal hopping under boundary perturbations of an interacting many-body system is not yet clear. In this work, we examine the boundary sensitivity of a non-Hermitian interacting fermionic system in the presence of a random disorder potential. A non-zero boundary parameter results in real-complex spectral transitions with non-reciprocal (or unidirectional) hopping at weak disorder. While the many-body localization at strong disorder washes away real-complex transitions leading to dynamical stability and real eigenvalue spectrum. We show that the boundary-driven real-complex spectral transitions of the non-Hermitian chain are accompanied by the corresponding changes in the level statistics and nearest level-spacing distributions. The intriguing features of non-reciprocity and boundary sensitivity are further revealed using the averaged inverse participation ratios. Finally, we find distinct behaviour in the quench dynamics of local particle density, population imbalance, and entanglement entropy of charge-density-wave ordered state that corroborate the real-complex and localization transitions. Our results provide a route to understanding disordered many-body systems under a generalized boundary.