Random two-body dissipation induced non-Hermitian many-body localization

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 (H) over cap = Sigma(L-1)(j) [-J ((b) over cap (+)(j)(b) over cap (j+1) + (b) over cap (+)(j+1)(b) over cap (j)) + 1/2(U - i gamma(j))(n) over cap (j)(n) over cap (j+1)) with the random two-body loss gamma(j) is an element of[0, W]. By the level statistics, the system undergoes a transition from the AI 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) <(r) over bar > ((-< cos theta >) over bar 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 <(S) over bar > 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 <(S(t))over bar> shows logarithmic growth. However, when t >= 10(2), <(S(t))over bar> can stabilize and tend to the steady-state half-chain entanglement entropy (S-0) over bar. The results of the dynamical evolution of <(S(t))over bar> imply that one can detect the occurrence of the non-Hermitian MBL by the short-time evolution of <(S(t))over bar>, and the long-time behavior of <(S(t))over bar> signifies the steady-state information.