Search for bose glass phase in the Shastry-Sutherland model
Physicists are interested on the physical properties during the phase transition of lattices under various Hamiltonian model. In this project, we are dealing with the hard core boson in the Shastry-Sutherland model under the Bose-Hubbard Hamiltonian model, where the diagonal bonds and square (vertic...
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| 格式: | Final Year Project |
| 語言: | English |
| 出版: |
2014
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| 在線閱讀: | http://hdl.handle.net/10356/60937 |
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| 機構: | Nanyang Technological University |
| 語言: | English |
| 總結: | Physicists are interested on the physical properties during the phase transition of lattices under various Hamiltonian model. In this project, we are dealing with the hard core boson in the Shastry-Sutherland model under the Bose-Hubbard Hamiltonian model, where the diagonal bonds and square (vertical and horizontal) bonds are of different strength. We only focus on the low temperature since we want to search its Bose glass phase. In this project, 4 physical properties are determined: boson density, structure factor, stiffness and energy, by using the one of the quantum Monte Carlo methods called the \emph{stochastic series expansion}.
Stochastic series expansion was studied thoroughly and instead of using the quantum states $\alpha$, it uses $\left\{ \alpha,S_{M}\right\} $ as the sample configuration where $S_{M}$ is the set of permutation of $M$ bond operators. The Monte Carlo simulation, which consists of 3 types of updates (namely diagonal update, off-diagonal/loop update and site update), was written by \CC and it was verified with the analytical solution of $2\times2$ lattice.
It was realised that the system consists of 3 different states: dimer, checkerboard and superfluid, where superfluid lies as the ``intermediate state'' between dimer and checkerboard. |
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