This dissertation describes a theoretical study of strongly correlated electron systems. We present a variational quantum Monte Carlo approach based on matrix-product states, which enables us to naturally extend our work into higher-dimensional tensor-network states as well as to determine the ground state and the low-lying excitations of quasi-onedimensional electron systems. Our results show that the ground state of the quarterilled zigzag electron ladder is expected to exhibit a bond distortion whose pattern is not affected by the electron-electron interaction strength. This dissertation also presents a new method that combines a quantumMonte Carlo technique with a class of tensor-network states. We show that this method can be applied to two-dimensional fermionic or frustrated models that suffer from a sign problem. Monte Carlo sampling over physical states reveals better scaling with the size of matrices under periodic boundary conditions than other types of higher-dimensional tensor-network states, such as projected entangled-pair states, which lead to unfavorable exponential scaling in the matrix size.
| Identifer | oai:union.ndltd.org:MSSTATE/oai:scholarsjunction.msstate.edu:td-4705 |
| Date | 12 May 2012 |
| Creators | Song, Jeong-Pil |
| Publisher | Scholars Junction |
| Source Sets | Mississippi State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Theses and Dissertations |
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