Year: 2024
Type: article
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 \begin{document}$ \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,$\end{document} with the random two-body loss \begin{document}$\gamma_j\in\left[0,W\right]$\end{document} . By the level statistics, the system undergoes a transition from the AI \begin{document}$^{\dagger}$\end{document} symmetry class to a two-dimensional Poisson ensemble with the increase of disorder strength. This transition is accompanied by the changing of the average magnitude (argument) \begin{document}$\overline{\left\langle {r}\right\rangle}$\end{document} ( \begin{document}$\overline{-\left\langle \cos {\theta}\right\rangle }$\end{document} ) of the complex spacing ratio, shifting from approximately 0.722 (0.193) to about 2/3 (0). The normalized participation ratios of the majority of eigenstates exhibit finite values in the ergodic phase, gradually approaching zero in the non-Hermitian MBL phase, which quantifies the degree of localization for the eigenstates. For weak disorder, one can see that average half-chain entanglement entropy \begin{document}$\overline{\langle S \rangle}$\end{document} follows a volume law in the ergodic phase. However, it decreases to a constant independent of L in the deep non-Hermitian MBL phase, adhering to an area law. These results indicate that the ergodic phase and non-Hermitian MBL phase can be distinguished by the half-chain entanglement entropy, even in non-Hermitian system, which is similar to the scenario in Hermitian system. Finally, for a short time, the dynamic evolution of the entanglement entropy exhibits linear growth with the weak disorder. In strong disorder case, the short-time evolution of \begin{document}$\overline{S(t)}$\end{document} shows logarithmic growth. However, when \begin{document}$t\geqslant10^2$\end{document} , \begin{document}$\overline{S(t)}$\end{document} can stabilize and tend to the steady-state half-chain entanglement entropy \begin{document}$\overline{ S_0 }$\end{document} . The results of the dynamical evolution of \begin{document}$\overline{S(t)}$\end{document} imply that one can detect the occurrence of the non-Hermitian MBL by the short-time evolution of \begin{document}$\overline{S(t)}$\end{document} , and the long-time behavior of \begin{document}$\overline{S(t)}$\end{document} signifies the steady-state information.
Source: Acta Physica Sinica
Authors: Jing-Hu Liu, Zhi-Hao Xu
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Award: G5832151869
OpenAlex ID: W4390978274