UC Santa Barbara

We begin with an introduction to some of the important numerical tools in the field of condensed matter theory:

exact diagonalization, quantum Monte Carlo, and tensor network algorithms. We also introduce interesting problems

to which they can be applied, including holographic duals (for tensor networks), many-body localization,

and thermalization.

We explore, using the previously discussed quantum Monte Carlo methods, a model of itinerant interacting fermions

with relevance to the mysterious pseudogap phase of the cuprate high temperature superconductors. We provide tentative

evidence for a non-Fermi liquid phase believed to support a violation of area law entanglement scaling. We hope to

settle numerical questions about this work in furtherance of the goal of incorporating it into a future publication.

We then explore the stability of a system predisposed towards localization coupled to a system of similar size which would,

on its own, thermalize. The stability of localized systems interacting with environmental baths is both experimentally

relevant and theoretically interesting, and we explore a large parameter space using exact diagonalization techniques.

We find that for a small set of parameters, localization may survive the presence of a similarly sized bath, but the

tendency of the bath to delocalize the entire system is difficult to overcome. We also investigate the dynamics of

these coupled systems, making connections with previous theoretical studies. This work is adapted from previously published

material.

We take steps towards developing a new tensor network technique with which to study non-equilibrium quantum systems.

We develop a disentangling circuit generation algorithm, drawing on previous algorithms for representing a variety of

interesting wavefunctions, which can disentangle generic states without reference to a Hamiltonian. This is a novel departure

from many previous disentangling approaches or tensor network optimization algorithms. We apply this technique to well-understood

physics in the form of disordered models of free fermions, detecting an emergent entanglement geometry which reproduces

interesting features of holographic duality. This work is also adapted from a previous publication.

We then extend these results to the realm of dynamics, investigating the effects of quantum quenches on the circuits generated by the disentangling algorithm and the role disorder may play. We find an intriguing connection between disorder strength and the effective energy density (or effective ``temperature''). We also observe two regimes, one as the system approaches its volume law limit, and another of slowly decaying oscillations after it has reached the long-time regime of volume law entanglement scaling. We hope to develop this last set of results into a future publication.