Date of Degree
PhD (Doctor of Philosophy)
First Committee Member
Second Committee Member
Third Committee Member
Fourth Committee Member
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.
Gauge, Lattice, Optical lattice, Quantum Simulation, Renormalization
xii, 182 pages
Includes bibliographical references (pages 170-182).
Copyright © 2017 Judah Francis Unmuth-Yockey
Unmuth-Yockey, Judah Francis. "Duality methods and the tensor renormalization group: applications to quantum simulation." PhD (Doctor of Philosophy) thesis, University of Iowa, 2017.