UC Berkeley

This dissertation studies the persistence of localization and nonergodicity in quantum many-body systems upon collectively coupling a localized bath to a central degree of freedom. Our work sits at the crossroads between two branches of inquiry that are currently under intense theoretical and experimental scrutiny: the existence of robust nonequilibrium phases of matter afforded by external driving or strong disorder, and how one can develop new computational approaches to study dynamics in large systems to long times. The latter is particularly poignant now that we have entered the age of ``noisy intermediate-scale'' quantum computers, scalable analog quantum simulators, and strongly correlated materials, all of which test the limits of what our current toolbox of numerical simulations can achieve. In this respect, centrally coupled systems offers a useful playground for designing new methods for dynamics due to its highly nonlocal geometry, which should generically lead to the rapid growth of entanglement.

In Chapter 2, we show how to avoid this scenario by ensuring that the bath stays localized even with finite central coupling. While one would intuitively expect that the presence of a central degree of freedom would mediate infinite ranged interactions between different parts of the localized bath and thereby destroying it, we demonstrate through analytical arguments and numerical simulations that this is not always true. This crucially relies on being able to suppress the effects of the mediated interactions by making the internal level spacing of the central degree of freedom large enough, at the same time that the number of internal levels is sufficiently large compared to the size of the bath. We give numerical evidence linking a small number of internal levels to the suppression of localization by examining eigenstate and spectral properties of a generic model with bath sizes up to 14 sites.

In Chapter 3, we attempt to probe what happens with much larger bath sizes by studying the dynamics of these localizable, centrally coupled systems using a method based on the time-dependent variational principle. The method is most effective deep in the localized phase, which allows us to study baths of size ~10^2 sites as well as interesting slow dynamics on intermediate timescales reminiscent of logarithmic growth of entanglement in one-dimensional many-body localized systems. Finally, we apply preliminary results on a controlled expansion for the propagator to attempt to understand some of the dynamics revealed by numerical simulations. However, both the numerical and analytical approaches are found to be limited to finite timescales which, in the case of the numerical method, is sometimes due to the rapid growth of entanglement.

In Chapter 4, we strive to push past the limited timescales by focusing on the dynamics of only the system. We study the time-nonlocal memory kernel for the population dynamics of the central degree of freedom, which is again coupled to a localizable bath. We analyze its behavior on short, intermediate, and long timescales to understand what signatures, if any, a localized bath imparts on the memory kernel. From our analysis on the long time behavior, we demonstrate how one can use the memory to directly extract infinite time values for the population from finite time simulations, and potentially serving as a useful approach to obtaining longer time dynamics without directly simulating them.