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

  • Author / Creator
    Graves, Christopher
  • 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.

  • Subjects / Keywords
  • Graduation date
    2011-11
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R35G9N
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Physics
  • Supervisor / co-supervisor and their department(s)
    • Beach, Kevin (Physics)
  • Examining committee members and their departments
    • Hanna, Gabriel (Chemistry)
    • Marsiglio, Frank (Physics)
    • Dumberry, Mathieu (Physics)
    • Davis, John (Physics)