Type
Text
Type
Dissertation
Advisor
Korepin, Vladimir E | Wei, Tzu-Chieh | Schneble, Dominik | Sutherland, Scott.
Date
2015-12-01
Keywords
Algebraic Bethe Ansatz, Heisenberg model, Hubbard model, Numerics, Spin chain, Tensor Network | Physics
Department
Department of Physics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76686
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
We consider several exactly solvable models of strongly correlated electrons in one dimension, such as the Heisenberg XXX model, the supersymmetric t-J model and the Hubbard model. These models can be solved by using the method of graded algebraic Bethe ansatz. We use it to design graded tensor networks which can be contracted approximately to obtain a Matrix Product State. This overcomes a major shortcoming of current density matrix renormalization group (DMRG) methods which work well on the ground states, but have difficulty working with the excited states of such models. In addition, observables such as correlation functions are important as they are experimentally measurable, but have been analytically described in the double scaling limit only. Moreover, these analytical results are mostly expressed in the form of determinants, which are numerically inefficient to compute. With the tensor network description of the spin models, we can efficiently compute any expectation value of the eigenstates on finite length lattices for direct comparison with laboratory results. As a proof of principle, we calculate correlation functions of ground states and excited states of such models on finite lattices of lengths in an intermediate regime which are of experimental interest. | 108 pages
Recommended Citation
Chong, You Quan, "Algebraic Bethe Ansatz and Tensor Networks" (2015). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2570.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2570