Random Two-Body Dissipation Induced the Non-Hermitian Many-Body Localization

Abstract

Recent studies on disorder-driven many-body localization (MBL) in non-Hermitian quantum systems have attracted great interest. We investigate the non-Hermitian MBL in a one-dimensional hard-core Bose model induced by random two-body dissipation, which is described by \begin{equation} \hat{H}=\sum_{j}^{L-1}\left[ -J\left( \hat{b}_{j}^{\dag}\hat{b}_{j+1}+\hat {b}_{j+1}^{\dag}\hat{b}_{j}\right) +\frac{1}{2}\left( U-i\gamma_{j}\right) \hat{n}_{j}\hat{n}_{j+1}\right] \notag, \end{equation} with the random two-body loss $\gamma_j\in\left[0,W\right]$. By the level statistics, the system undergoes a transition from the AI$^{\dag}$ symmetry class to a two-dimensional Poisson ensemble with the increase of disorder strength. This transition is accompanied by changing of the average magnitude (argument) $\overline{\left\langle {r}\right\rangle}$ ($\overline{-\left\langle \cos {\theta}\right\rangle }$) of the complex spacing ratio, shifting from approximately $0.722$ (0.193) to about $2/3$ (0). The normalized participation ratios of the majority of eigenstates exhibit finite values in the ergodic phase, gradually approaching zero in the non-Hermitian MBL phase, which quantifies the degree of localization for the eigenstates. For weak disorder, one can see that average half-chain entanglement entropy $\overline{\langle S \rangle}$ follows a volume law in the ergodic phase. However, it decreases to a constant independent of $L$ in the deep non-Hermitian MBL phase, adhering to an area law. These results indicate that the ergodic and non-Hermitian MBL phases can be distinguished by the half-chain entanglement entropy, even in non-Hermitian systems, similar to the Hermitian cases. Finally, for a short time, the dynamic evolution of the entanglement entropy exhibits linear growth with the weak disorder. In strong disorder cases, the short-time evolution of $\overline{S(t)}$ shows linear growth. However, when $t\geq10^2$, $\overline{S(t)}$ can stabilize and tend to the steady-state half-chain entanglement entropy $\overline{ S_0 }$. The results of the dynamical evolution of $\overline{S(t)}$ imply that one can detect the occurrence of the non-Hermitian MBL by the short-time evolution of $\overline{S(t)}$, and the long-time behavior of $\overline{S(t)}$ signifies the steady-state information.