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Computational study of frustrated magnets and disordered bosons Open Access


Other title
quantum spin liquid
phase transition
Monte Carlo simulation
frustrated magnets
disordered Bose-Hubbard model
multisite mean-field theory
Type of item
Degree grantor
University of Alberta
Author or creator
Xu, Jin
Supervisor and department
Beach, Kevin (Physics)
Examining committee member and department
Davis, John (Physics)
Frei, Christoph (Mathematical and Statistical Sciences)
Marsiglio, Frank (Physics)
Department of Physics

Date accepted
Graduation date
Master of Science
Degree level
Quantum many-body systems have played a significant role in modern condensed matter physics. In exploring such systems, computational simulation has been an important complement to experimental and field-theoretic approaches. In this thesis, we focus on two projects---worm Monte Carlo study of frustrated magnets and mean-field approach to disordered bosons. In the first project, we construct a family of short-range resonating-valence-bond wave functions on a layered cubic lattice, allowing for a tunable anisotropy in the amplitudes assigned to nearest-neighbour valence bonds along one axis. Monte Carlo simulations reveal that four phases are stabilized over the full range of the anisotropy parameter. They are separated from one another by a sequence of continuous quantum phase transitions. An antiferromagetic phase, centered on the perfect isotropy point, intervenes between two {\em distinct} quantum spin liquid states. One of them is continuously deformable to the two-dimensional $U(1)$ spin liquid, which is known to exhibit critical bond correlations. The other has both spin and bond correlations that decay exponentially. It indicates the existence of a fully gapped spin liquid in three dimensions, which may exhibit topological order. In the second project, we study the two-dimensional disordered Bose-Hubbard model by means of both single-site and cluster mean field approaches. The many-body Hamiltonian is decomposed into a summation over isolated local Hamiltonians via replacing the nearest-neighbour hopping with an effective mean-field parameters. A self-consistent set of mean-field parameters are obtained in an iteration process. An important innovation in our work is that, the percolation of superfluid clusters embedded in the insulating background is quantified by mapping the disordered system onto a classical resistor network. With potential disorder present, Bose glass phase always intervenes between Mott-insulator and superfluid phases and no direct transition from Mott-insulator to superfluid is found at $\Delta / U = 0.6$. A simple calculation with $2 \times 2$ cluster mean-field method is carried out. Compared with single-site mean-field method, it gives bigger values for both critical points, $J_1$ and $J_2$. Since the spatial symmetries are absent, we propose a sophisticated way of partitioning the lattice into clusters in different shapes and of different sizes, based on the rank of bonds.
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 these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before 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.
Citation for previous publication
Jin Xu and K. S. D. Beach, “Two distinct spin liquid states in a layered cubic lattice,” arXiv eprints, 1311.0004v1.

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