Kwek, Leong Chuan

It is known that strong disorder in closed quantum systems leads to many-body localization (MBL), and that this quantum phase can be destroyed by coupling to an infinitely large Markovian environment. However, the stability of the MBL phase is less clear when the system and environment are of finite and comparable size. Here, we study the stability and eventual localization properties of a disordered Heisenberg spin chain coupled to a finite environment, and extensively explore the effects of environment disorder, geometry, initial state, and system-bath coupling strength, using the steady-state value of magnetization as a probe. Focusing on nonequilibrium dynamics and steady-state properties, our results indicate that within system sizes amenable to exact diagonalization, a strongly localized system interacting in a junction configuration retains remnant information on its initial state at long times despite coupling to a finite ergodic environment. In contrast, in a ladder configuration, strong dependencies on the initial state and coupling strength are observed, which can lead to either the loss or retention of information. Finally, we highlight and discuss discrepancies that can arise when similar methodologies are employed to infer localization or thermalization, revealing the need for careful interpretation.

Conventional many-body quantum systems thermalize under their own dynamics, losing information about their initial configurations to the environment. However, it is known that a strong disorder results in many-body localization (MBL). A closed quantum systems with MBL retains local information even in the presence of interactions. Here, we numerically study the propagation and scrambling of quantum information of a closed system in the MBL phase from an information theoretic perspective. By simulating the dynamics and equilibration of the temporal mutual information for long times, we see that it can distinguish between MBL and ergodic phases.