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- W2950448077 abstract "Author(s): Hyatt, Katharine Sarah | Advisor(s): Fisher, Matthew P. A.; Bauer, Bela | Abstract: 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 problemsto 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 fermionswith relevance to the mysterious pseudogap phase of the cuprate high temperature superconductors. We provide tentativeevidence for a non-Fermi liquid phase believed to support a violation of area law entanglement scaling. We hope tosettle 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 experimentallyrelevant 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 thetendency of the bath to delocalize the entire system is difficult to overcome. We also investigate the dynamics ofthese coupled systems, making connections with previous theoretical studies. This work is adapted from previously publishedmaterial.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 ofinteresting wavefunctions, which can disentangle generic states without reference to a Hamiltonian. This is a novel departurefrom many previous disentangling approaches or tensor network optimization algorithms. We apply this technique to well-understoodphysics in the form of disordered models of free fermions, detecting an emergent entanglement geometry which reproducesinteresting 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." @default.
- W2950448077 created "2019-06-27" @default.
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- W2950448077 date "2018-01-01" @default.
- W2950448077 modified "2023-09-23" @default.
- W2950448077 title "Numerical Investigations of Many-Body Localization and non-Fermi Liquids" @default.
- W2950448077 hasPublicationYear "2018" @default.
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