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

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Sienko, Tanya Christine

Contributors dc:contributor

• Kogut, John B.

• Physics, Condensed Matter
• Physics, Elementary Particles and High Energy

Statement dc:rights

• Copyright 1995 Sienko, Tanya Christine

Language dc:language

eng

Identifier

AAI9543722
(UMI)AAI9543722

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/22005