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Opponent: Professor Fabian Heidrich-Meisner,
Supervisor: Professor Jens H. Bardarson, Kondenserade materiens teori
A many-body quantum system has the potential for entanglement between its subsystems---a form of correlation that has no equivalent in classical physics. A key feature of a many-body quantum system is the potential for entanglement between its subsystems---a form of correlation that has no equivalent in classical physics. Due to entanglement, the calculation of quantum mechanical processes generally requires resources that grow exponentially with the system size. This prevents exact simulations of generic interacting quantum systems for large system sizes and long timescales on classical computers, which leaves many questions open in this domain.
In this thesis, we investigate thermalization and localization in closed quantum systems, which are processes in which entanglement either proliferates or is exponentially suppressed. In both cases, we can make progress on classical computers by systematically discarding non-essential entanglement information to obtain approximate results that are nevertheless meaningful. We present several algorithms that follow this principle, some of which we developed from the ground up, while others improve upon existing methods.
We employ the recently developed information lattice---a spatially hierarchical decomposition of the quantum information in a state---to track the location of information over time and space, supplementing conventional measures based on the entanglement entropy. The information lattice underpins our Local Information Time Evolution (LITE) algorithm, which continually separates and discards large scale thermal information as it arises, from the local information that is relevant for physical observables. It also sheds light on the Density Matrix Renormalization Group (DMRG) algorithm, aiding our efforts to improve the convergence process when calculating highly excited states. Furthermore, we use the information lattice as the basis for a new universal characterization of quantum matter, whether thermal or localized.
Finally, we introduce a random circuit model of interacting local integrals of motion (l-bits), to simulate the dynamics of effective quantum systems that are localized by definition. We use this model to investigate whether slow particle transport can exist in localized systems. Since the prevailing belief has been that slow particle transport is impossible in localized systems, recent numerical evidence of such transport sparked a debate as to whether localization can exist as a macroscopic phenomenon. By reproducing those results with our model, we show that the observation of slow particle transport is not sufficient to rule out the existence of localization.