Information Flow and Local Observables in Many Body Localized Systems

Sammanfattning: Disordered quantum many-body systems exhibiting the many-body localization (MBL) phenomenon evade the fate of thermalization due to the existence of an extensively large set of quasi-local integrals of motion (l-bits). Due to the size of the Hilbert space of many-body systems, it is hard to compute the time evolution of many-body systems generally, which hinders our understanding of the MBL phenomenon. Recently it has been proposed in Ref. [1] to time evolve local density matrices of lattice system with short-range interactions using the Petz recovery map. By time evolving local density matrices, information encoded in long-range entanglement that is irrelevant to the time-evolution of local observables is discarded. This method is promising for MBL-systems, primarily because it can be implemented to conserve local constants of the motion. For the case of a MBL system, this means that the l-bits can be (approximately) conserved. This thesis employs the Petz recovery map to time evolve local density matrices of localized 1D lattice systems, modeled by the Aubry-André Hamiltonian. The accuracy of the method is evaluated and the results are used to study the flow of information between subsystems. It is found that the method can accurately time evolve localized density matrices for an Anderson localized system to arbitrary times. For interacting systems, it is shown that the method is accurate for long time if the system is sufficiently localized. Furthermore, the solutions for the local density matrices exhibit the information spread behavior that is predicted by the l-bit theory of the many-body localized phase: both the logarithmic ”light” cone of entanglement and the dephasing dynamics are observed. This work shows that time evolution of local density matrices is a promising method in the pursuit of a better understanding of the nature of localized systems.