#### Title

The open spin-½ XXZ quantum spin chain

#### Date of Award

2007

#### Availability

Article

#### Degree Name

Doctor of Philosophy (Ph.D.)

#### Department

Physics

#### First Committee Member

R. I. Nepomechie, Committee Chair

#### Abstract

Bethe Ansatz solutions of the open spin-1/2 integrable XXZ quantum spin chain at roots of unity with nondiagonal boundary terms containing two free boundary parameters have been proposed. We use these solutions to compute the boundary energy (surface energy) in the thermodynamic limit.We propose a Bethe-Ansatz-type solution of the open spin-1/2 integrable XXZ quantum spin chain with general integrable boundary terms and bulk anisotropy values ipi/(p + 1), where p is a positive integer. All six boundary parameters are arbitrary, and need not satisfy any constraint. The solution is in terms of generalized T - Q equations, having more than one Q function. We find numerical evidence that this solution gives the complete set of 2N transfer matrix eigenvalues, where N is the number of spins.We use this solution (with general integrable boundary terms and bulk anisotropy values ipi/(p+1)), together with an appropriate string hypothesis, to compute the boundary energy of the chain in the thermodynamic limit.

#### Keywords

Physics, Theory

#### Recommended Citation

Shi, Chi, "The open spin-½ XXZ quantum spin chain" (2007). *Dissertations from ProQuest*. 2533.

https://scholarlyrepository.miami.edu/dissertations/2533

## Link to Full Text

http://access.library.miami.edu/login?url=http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3267726