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

• Author / Creator

  Zhang, Xiaoming

• 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.

• Subjects / Keywords

  • Frustrated Heisenberg model
  • Square lattice
  • Monte Carlo
  • Phase transition
  • Trial wavefunction

• Graduation date

  Fall 2011

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3R614

• 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.