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.
Dissertation
Duality methods and the tensor renormalization group: applications to quantum simulation
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Summer 2017
DOI: 10.17077/etd.2b73kaef
Abstract
Details
- Title: Subtitle
- Duality methods and the tensor renormalization group: applications to quantum simulation
- Creators
- Judah Francis Unmuth-Yockey - University of Iowa
- Contributors
- Yannick Meurice (Advisor)Michael Flatte (Committee Member)Vincent Rodgers (Committee Member)Wayne Polyzou (Committee Member)James Osborn (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Physics
- Date degree season
- Summer 2017
- DOI
- 10.17077/etd.2b73kaef
- Publisher
- University of Iowa
- Number of pages
- xii, 182 pages
- Copyright
- Copyright © 2017 Judah Francis Unmuth-Yockey
- Language
- English
- Description illustrations
- color illustrations
- Description bibliographic
- Includes bibliographical references (pages 170-182).
- Public Abstract (ETD)
Modern scientific computing has certain limitations when it comes to calculations with many-body quantum systems. A possible solution to this problem is the idea of quantum computing, or quantum simulation, suggested by Richard Feynman. Here, the actual computer used to calculate is itself a quantum system, overcoming the limitations from regular computers. In this thesis we discuss mathematical methods, specifically the tensor renormalization group, which allow one to understand and possibly create a particular kind of quantum simulator using very cold atoms trapped in a lattice made of laser light. We do this for a few physically relevant models and discuss possible future directions the research could take.
- Academic Unit
- Physics and Astronomy
- Record Identifier
- 9983776929702771
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