Quantum Monte Carlo Simulations of Fermion Systems with Matrix Product States


Clay, R. Torsten

Committee Member

Novotny, Mark A.

Committee Member

Afanasjev, Anatoli

Committee Member

Banicescu, Ioana

Committee Member

Monts, David L.

Date of Degree


Original embargo terms

MSU Only Indefinitely

Document Type

Dissertation - Open Access


Engineering with an Emphasis in Applied Physics

Degree Name

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.




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

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