Date of Award

9-25-2018

Degree Type

Thesis

Degree Name

M.Sc.

Department

Physics

First Advisor

Kim, Eugene

Keywords

Charge Fluctuations, Condensed Matter, Entanglement, Haldane Model, Quantum Quench, Topological Insulator

Rights

CC-BY-NC-ND

Abstract

Topological insulators are materials that behave like an insulator in the bulk but have conducting edge states. These edge states are topologically protected and exhibit unique properties. Studying the dynamics of these systems far-from equilibrium can provide information on the stability of these edge states and provide insight on the propagation of entanglement which is of interest in quantum information. In this thesis, I study the far-from-equilibrium dynamics of the Haldane model. Various quenches between different topological phases are performed, and the dynamics of both the entanglement and particle numbers are analyzed. Using a correlation matrix, the time evolution of the entanglement and charge fluctuations are calculated. The dynamics of the entanglement and charge fluctuations provides insight on the evolution of this system following a quench. The charge fluctuations allow us to probe the entanglement of these systems using a quantity that can be measured experimentally. I showed that for the various quenches, the charge fluctuations mirrors the entanglement entropy providing examples for which the second moment provides the majority of the weight. Additionally, I showed that the entanglement entropy drastically increases immediately following a quench until the system reaches a steady state. By analyzing the entanglement spectrum I showed that the bulk states contribute to the entanglement following a quench. This thesis establishes a framework that can be applied to other topological systems.

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