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A trial wavefunction approach to the frustrated square-lattice Heisenberg model Open Access


Other title
phase transition
Monte Carlo
square lattice
frustrated Heisenberg model
trial wavefunction
Type of item
Degree grantor
University of Alberta
Author or creator
Zhang, Xiaoming
Supervisor and department
Beach, Kevin (Physics)
Examining committee member and department
Czarnecki, Andrzej (Physics)
Brown, Alexander (Chemistry)
Freeman, Mark (Physics)
Currie, Claire (Physics)
Department of Physics

Date accepted
Graduation date
Master of Science
Degree level
Models of interacting quantum spins have contributed significantly to our understanding of magnetism. The Heisenberg model on square lattice, which exhibits semiclassical N´eel order, is one of the canonical models. However, with frustration introduced by competing interactions, the system becomes computationally intractable. Exotic quantum phases that have no magnetic long range order may be present due to the frustration. The quantum phases do not have any classical analogue, and a valence bond crystal state with translational and/or rotational symmetry breaking as well as a quantum spin liquid state have been proposed as potential candidates. We construct several trial wavefunctions in the resonating valence bond basis and apply large-scale unbiased calculations to examine the possible descriptions of the ground state in the strongly frustrated region. An analytical master equation is also proposed to provide an approximate solution for the valence bond states. Our numerical and analytical studies suggest that the frustrated ground state exhibits a one-dimensional-like behaviour.
License granted by Xiaoming Zhang ( on 2011-08-31T18:19:12Z (GMT): Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of the above terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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File title: Introduction
File title: A trial wavefunction approach to the frustrated square-lattice Heisenberg model, M. Sc. Thesis
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