Theses and Dissertations

Issuing Body

Mississippi State University

Advisor

Clay, R. Torsten

Committee Member

Novotny, Mark A.

Committee Member

Afanasjev, Anatoli

Committee Member

Banicescu, Ioana

Committee Member

Monts, David L.

Date of Degree

5-12-2012

Original embargo terms

MSU Only Indefinitely

Document Type

Dissertation - Campus Access Only

Major

Applied Physics

Degree Name

Doctor of Philosophy

College

James Worth Bagley College of Engineering

Department

Applied Physics Program

Abstract

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.

URI

https://hdl.handle.net/11668/19353

Comments

matrix product states||Quantum Monte Carlo||Hubbard model

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