Date of Award

5-12-2024

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics

Advisor(s)

Simon Catterall

Keywords

Lattice Supersymmetry;Quantum Computing

Subject Categories

Physical Sciences and Mathematics | Physics

Abstract

In this thesis, we aim to develop classical and quantum simulations to test holography. Holography can be thought of in its most basic form as a duality that relates a d + 1 dimensional theory to a d dimensional one and the most famous holographic correspondence is the AdS/CFT duality where d + 1 dimensional weakly coupled gravity theory is related to a d dimensional CFT. We start by developing lattice simulations for the N = 4 super Yang-Mills model and explore an improved supersymmetric lattice action showing that it is free of the lattice artifacts that plagued earlier lattice theories. We use it to calculate supersymmetric Wilson loops and the non-Abelian Coulomb potential using Polyakov line correlators. For both of these observables, we demonstrate the excellent agreement between lattice results and analytical results obtained from the holographic dual. This constitutes a very non-trivial check for the AdS/CFT correspondence using non-perturbative classical simulation methods. In the latter part of this thesis, we extend these ideas to quantum simulations for a simpler class of model the transverse Ising Model living in an AdS2 space. We obtain the ground state of this model and explore the phase structure of the theory using the Density Matrix Renormalization Group (DMRG) . We then obtain the time-evolution of this system using both classical methods such as Time Evolving Block Decimation (TEBD) and usual quantum simulation techniques. The most interesting aspects of this model appear when we calculate the out-of-time-ordered correlators (OTOCs) to investigate the information propagation and scrambling in this model. We find a region where these OTOCs have a logarithmic dependence on the number of degrees of freedom of the system. This behavior has only been seen previously for models that are all to all or have infinite or long-range interactions. Yet our simple model with only nearest-neighbor interactions manages to capture this behavior. This makes this model a very interesting candidate to study information propagation and scrambling using quantum simulations.

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