#### Publication Date

2008-04-12

#### Availability

Open access

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy (PHD)

#### Department

Physics (Arts and Sciences)

#### Date of Defense

2008-04-04

#### First Committee Member

Rafael I. Nepomechie - Committee Chair

#### Second Committee Member

James Nearing - Committee Member

#### Third Committee Member

Orlando Alvarez - Committee Member

#### Fourth Committee Member

Changrim Ahn - Outside Committee Member

#### Abstract

The open spin-1/2 XXZ quantum spin chain with general integrable boundary terms is a fundamental integrable model. Finding a Bethe Ansatz solution for this model has been a subject of intensive research for many years. Such solutions for other simpler spin chain models have been shown to be essential for calculating various physical quantities, e.g., spectrum, scattering amplitudes, finite size corrections, anomalous dimensions of certain field operators in gauge field theories, etc. The first part of this dissertation focuses on Bethe Ansatz solutions for open spin chains with nondiagonal boundary terms. We present such solutions for some special cases where the Hamiltonians contain two free boundary parameters. The functional relation approach is utilized to solve the models at roots of unity, i.e., for bulk anisotropy values eta = i pi/(p+1) where p is a positive integer. This approach is then used to solve open spin chain with the most general integrable boundary terms with six boundary parameters, also at roots of unity, with no constraint among the boundary parameters. The second part of the dissertation is entirely on applications of the newly obtained Bethe Ansatz solutions. We first analyze the ground state and compute the boundary energy (order 1 correction) for all the cases mentioned above. We extend the analysis to study certain excited states for the two-parameter case. We investigate low-lying excited states with one hole and compute the corresponding Casimir energy (order 1/N correction) and conformal dimensions for these states. These results are later generalized to many-hole states. Finally, we compute the boundary S-matrix for one-hole excitations and show that the scattering amplitudes found correspond to the well known results of Ghoshal and Zamolodchikov for the boundary sine-Gordon model provided certain identifications between the lattice parameters (from the spin chain Hamiltonian) and infrared (IR) parameters (from the boundary sine-Gordon S-matrix) are made.

#### Keywords

Integrable Models; Bethe Ansatz; Quantum Spin Chain

#### Recommended Citation

Murgan, Rajan, "Bethe Ansatz and Open Spin-1/2 XXZ Quantum Spin Chain" (2008). *Open Access Dissertations*. 69.

http://scholarlyrepository.miami.edu/oa_dissertations/69