Quantum Monte Carlo Simulations of Fermion Systems with Matrix Product States
Clay, R. Torsten
Novotny, Mark A.
Monts, David L.
Date of Degree
Original embargo terms
MSU Only Indefinitely
Dissertation - Open Access
Engineering with an Emphasis in Applied Physics
Doctor of Philosophy
College of Arts and Sciences
Department of Physics and Astronomy
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.
Song, Jeong-Pil, "Quantum Monte Carlo Simulations of Fermion Systems with Matrix Product States" (2012). Theses and Dissertations MSU. 3706.