University of Illinois Urbana-Champaign

Dual mappings and phase transitions in a short-range random valence bond theory

Sienko, Tanya Christine

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Description

Title
Dual mappings and phase transitions in a short-range random valence bond theory
Author(s)
Sienko, Tanya Christine
Issue Date
1995
Doctoral Committee Chair(s)
Kogut, John B.
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Physics, Condensed Matter
  • Physics, Elementary Particles and High Energy
Language
eng
Abstract
This thesis describes calculations done in 3-D Short-Range Random Valence Bond theory. After reviewing the background of SRRVB and how it can be derived, I cover the technique of dual mappings, with a particular emphasis on the Compact U(1) model, the monopole loop gas picture, and the confinement/deconfinement phase transition. The argument is then made that an equivalent phase transition may exist in the 3-D SRRVB, based on its mapping onto a similar monopole loop gas picture, albeit complicated by the presence of Berry phases. Building on results from the 2-D model, I also argue for the existence of a second phase transition; this being the melting from a Valence-Bond Crystal to a Quantum Spin Liquid. To demonstrate the existence of one or both of these phase transitions, I have proformed numerical simulations using Monte Carlo. The confinement/deconfinement phase transition is tracked using both hysteresis and Wilson loop measurements, starting from the Compact U(1) model and slowly modifying the background and the anisotropy. The VBC/QSL phase transition is investigated by direct modeling of the J-V version of the SRRVB and measuring various correlation functions.
Type of Resource
text
Permalink
http://hdl.handle.net/2142/22005
Copyright and License Information
Copyright 1995 Sienko, Tanya Christine

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