Non-Hermitian Many-Body Localization with Open Boundaries

TL;DR

This paper investigates how non-Hermitian effects and boundary conditions influence many-body localization, revealing complex spectral transitions, suppression of skin effects, and distinctive dynamical signatures in non-Hermitian disordered systems.

Contribution

It uncovers the interplay between non-Hermitian skin effects and many-body localization, identifying boundary-dependent spectral transitions and characterizing wavefunction localization.

Findings

Two spectral transitions identified, one boundary-independent and one boundary-dependent.

Suppression of skin effects in the non-Hermitian MBL phase.

Dynamical signatures such as particle density and entanglement entropy reflect boundary effects.

Abstract

The explorations of non-Hermiticity have been devoted to investigate the disorder-induced many-body localization (MBL). However, the sensitivity of the spatial boundary conditions and the interplay of the non-Hermitian skin effect with many-body phenomena are not yet clear. For a MBL system in the presence of non-reciprocal tunnelings and random disorder potential, we identify two different complex-real spectral transitions, one is present for both open and periodic boundaries while the other is present only for open boundaries of a coupled non-Hermitian chains. The later is driven due to the inter-chain coupling at weak disorder where the level statistics of the real eigenenergy phase follows Gaussian orthogonal ensemble. We further characterize wavefunctions through the (biorthogonal) inverse participation ratio and fractal dimension, which reveal the suppression of skin effect in the non-Hermitian MBL phase. Finally, we demonstrate that the quench dynamics of the local particle density, spin imbalance, and entanglement entropy also signify the hallmark of the boundary effects and non-ergodic character of many-body localization.