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A generalized valence bond basis for the half-filled Hubbard model Open Access


Other title
exact diagonalization
Hubbard model
generalized valence bond basis
Type of item
Degree grantor
University of Alberta
Author or creator
Graves, Christopher
Supervisor and department
Beach, Kevin (Physics)
Examining committee member and department
Hanna, Gabriel (Chemistry)
Davis, John (Physics)
Dumberry, Mathieu (Physics)
Marsiglio, Frank (Physics)
Department of Physics

Date accepted
Graduation date
Master of Science
Degree level
I present a non-orthogonal and overcomplete set of states that spans the S_tot=0 Hilbert subspace for a fermionic system with four possible spin configurations per site, on a half-filled lattice with an even number of sites. This set consists of possible pairing of the spins into three bond types: singlet bonds and positive and negative charge bonds. Although I present the specific case for the half-filled Hubbard model in one-dimension, these sets of states can be trivially extended to higher dimensions. The overlap of these generalized valence bond states form closed loops with properties that are related to operator expectation values in this basis. I verify the correctness of this basis by solving the model via exact diagonalization and comparing with known results. There is evidence of structure in the ground state that may be useful to simulations using variational wave functions.
License granted by Chris Graves ( on 2011-09-23T14:10:23Z (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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