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Abstract

Recent researches on disorder-driven many-body localization (MBL) in non-Hermitian quantum systems have aroused great interest. In this work, we investigate the non-Hermitian MBL in a one-dimensional hard-core Bose model induced by random two-body dissipation, which is described by

$ \hat{H}=\displaystyle\sum\limits_{j}^{L-1}\left[ -J\left( \hat{b}_{j}^{\dagger}\hat{b}_{j+1}+\hat {b}_{j+1}^{\dagger}\hat{b}_{j}\right) +\frac{1}{2}\left( U-{\mathrm{i}}\gamma_{j}\right) \hat{n}_{j}\hat{n}_{j+1}\right] \notag,$

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 $^{\dagger}$ symmetry class to a two-dimensional Poisson ensemble with the increase of disorder strength. This transition is accompanied by the 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 Lin the deep non-Hermitian MBL phase, adhering to an area law. These results indicate that the ergodic phase and non-Hermitian MBL phase can be distinguished by the half-chain entanglement entropy, even in non-Hermitian system, which is similar to the scenario in Hermitian system. Finally, for a short time, the dynamic evolution of the entanglement entropy exhibits linear growth with the weak disorder. In strong disorder case, the short-time evolution of $\overline{S(t)}$ shows logarithmic growth. However, when $t\geqslant10^2$ , $\overline{S(t)}$ 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.

Keywords:

Authors and contacts

Liu Jing-Hu¹,
Xu Zhi-Hao^1,2

Corresponding author:Xu Zhi-Hao,xuzhihao@sxu.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 12375016), the Fundamental Research Program of Shanxi Province, China (Grant No. 20210302123442), the Beijing National Laboratory for Condensed Matter Physics, China, and the Fund for Shanxi “1331Project” Key Subjects, China.

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Vol. 73, Issue 7 - 2024-04-05

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