Advisory Committee Chair
Shannon Starr
Advisory Committee Members
David Halpern
Ryoichi Kawai
Nandor Simanyi
Dongsheng Wu
Document Type
Dissertation
Date of Award
2022
Degree Name by School
Doctor of Philosophy (PhD) College of Arts and Sciences
Abstract
The first part of this thesis covers some of the background materials that are prerequisite to doing research in many body particle problems. The definitions are given from a mathematical point of view and the proofs to most of the results were not included since they can be found in standard texts. The second part was done with Christoph Fischbacher. Here, we consider the Heisenberg XXZ spin-J chain (J ∈ N/2) with anisotropy parameter Δ. Assuming that Δ > 2J (a necessary but not sufficient condition), and introducing threshold energies EK := K (1 − 2J / Δ) , we show that the bipartite entanglement entropy (EE) of states belonging to any spectral subspace with energy less than EK+1 satisfy a logarithmically corrected area law with prefactor (2⌊K/J⌋ − 2). The third part is based on work done with Shannon Starr. We considered a spin-1/2 XXZ chain on the 1-D lattice of size N (even) and gave a lower bound for the ‘Emptiness Formation Probability’ when the anisotropy parameter Δ < 0. Also, we gave a slightly modified result for the upper bound of the ‘Emptiness Formation Probability’ for the case Δ < 1 as seen in [9].
Recommended Citation
Ogunkoya, Oluwadara, "Entanglement Entropy Bound and Emptiness Formation Probability of the XXZ Spin Chain" (2022). All ETDs from UAB. 358.
https://digitalcommons.library.uab.edu/etd-collection/358