Type
Text
Type
Dissertation
Advisor
Korepin, Vladimir | Wei, Tzu-Chieh | Kirillov, Alexander | Figueroa, Eden.
Date
2013-12-01
Keywords
Physics | Entanglement, Entanglement Spectrum, Many body physics, Reduced density matrix
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/11401/76727
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
In the ground state of gapped systems, the entanglement entropy of a subsystem A scales with the length of the boundary of A. This observation suggests that the entanglement properties of the sub- system can be described in terms of degrees of freedom living in the boundary of A. We will discuss the the connection between en- tanglement properties and effective boundary descriptions in spin systems in one and two dimensions. In one dimension we present analytic results for the spin S = 1, Affleck-Kennedy-Lieb-Tasaki (AKLT) ground state entanglement, characterized by negativity and entanglement spectrum. We also discuss a generalization of the AKLT model, based on the quantum group Uq (sl(2)) for gen- eral integer spin S. In two dimensions, we study two spin systems whose ground state can be written in terms of tensor product states of bond dimension two, the AKLT model in the hexagonal lattice and the Ising projected entangled pair state (Ising PEPS) in the square lattice. We show how the reduced density matrix of a parti- tion is associated with a thermal state of a one dimensional model along the boundary of that partition. We also present arguments supporting this correspondence for arbitrary gapped systems. Fi- nally we discuss the behavior of this boundary theory when the original two dimensional model is tuned through a quantum phase transition,126 pages
Recommended Citation
Santos, Raul, "Entanglement in low dimensional systems" (2013). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2608.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2608