Type
Text
Type
Thesis
Advisor
Rocek, Martin | Wei, Tzu-Chieh | Dawber, Matthew.
Date
2016-12-01
Keywords
Physics -- Theoretical physics -- Condensed matter physics | Ising Model, Quantum Entanglement, Quantum Information Theory, Quantum Phase Transition, Quantum XY Model, Statistical 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/11401/76636
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
In this work, we give a detailed analytic treatment of one-dimensional anisotropic XY model in the transverse field. We present a multipartite geometric measure of entanglement per site and per block and use it for quantifying global entanglement in many-body systems. We also investigate spontaneous symmetry breaking and Quantum Phase Transition (QPT) in the model. Further, we extend the solution of the XY model to the n-site interaction and diagonalize the Hamiltonian and obtain energy levels and eigenvalues. We also examine Quantum Entanglement and QPT for next-nearest neighbor interaction and halfway interaction. At last, we introduce a Generalized Cluster-XY Hamiltonian with n-site interaction. Through this, one can diagonalize many suitable bilinear Hamiltonians by defining parameters that characterize the model. By using the model, we investigate QPT between Ferromagnetic-Paramagnetic state, GHZ-Cluster state and symmetry protected topological order and an antiferromagnetic state. | 96 pages
Recommended Citation
Deger, Aydin, "Quantum Phase Transition and Quantum Entanglement in the Generalized Cluster-XY Model" (2016). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2525.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2525