Imaginary disorder-induced many-body localization and dynamical jumping

We present the non-Hermitian many-body localization (MBL) induced by imaginary disorder. By numerically calculating the entanglement entropy and complex level spacing, we identify a clear thermal-MBL transition: the entanglement entropy from the volume law to area law and the level spacing from the repulsive distribution to the uncorrelated Poisson distribution. In the complex energy plane, there exists a mobility loop separating different phases, which is similar to the mobility edge for the Hermitian MBL. Surprisingly, we find that the confluence of imaginary disorder and the localization length provides tunneling channels for dynamically jumping of the particles from the initial to the final state in both the real and Hilbert spaces. Our work provides an example of non-Hermitian many-body phases induced by imaginary disorder, which offers new possibilities for studying strongly correlated non-Hermitian physics.