DOI

10.17077/etd.2b73kaef

Document Type

Dissertation

Date of Degree

Summer 2017

Degree Name

PhD (Doctor of Philosophy)

Degree In

Physics

First Advisor

Meurice, Yannick

First Committee Member

Flatte, Michael

Second Committee Member

Rodgers, Vincent

Third Committee Member

Polyzou, Wayne

Fourth Committee Member

Osborn, James

Abstract

This thesis describes the duality methods used in the tensor renormalization group method and their application to quantum simulation with cold atoms in optical lattices. Here we consider specifically the O(2) and O(3) nonlinear sigma models in two dimensions, as well as the Abelian Higgs model in two dimensions. We give numerical results from the tensor renormalization group and comparisons with other numerical methods for all three models. We give proposals for possible experimental methods with which these models could be simulated using cold atoms trapped in optical lattices as is done in ongoing experiments.

Keywords

Gauge, Lattice, Optical lattice, Quantum Simulation, Renormalization

Pages

xii, 182 pages

Bibliography

Includes bibliographical references (pages 170-182).

Copyright

Copyright © 2017 Judah Francis Unmuth-Yockey

Included in

Physics Commons

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