Abstract/Details

Quasiparticles in quantum spin chains with strong axial exchange anisotropy


2009 2009

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Abstract (summary)

The quasiparticle composition of the eigenstates of quantum spin chains with nearest-neighbor exchange coupling subject to strong axial anisotropy is the focus of this dissertation. Complementary sets of quasiparticles are generated from opposite ends of the spectrum for the systematic generation of all eigenstates. The exclusion statistics of all quasiparticles thus introduced are determined exactly and used, in selected cases, for the exact thermodynamic analysis of the underlying spin chain model. This project starts from the Ising model with spin s = 1/2 and then branches out to the spin s = 1/2 XXZ model in the axial regime and to the spin s = 1 Ising model. In the s = 1/2 Ising case, the two complementary sets of quasiparticles are antiferromagnetic domain walls (solitons) and ferromagnetic domains (strings). In the s = 1 Ising case, they are soliton pairs and nested strings, respectively. The string quasiparticles of the s = 1/2 Ising chains are identified as limiting cases of Bethe ansatz solutions of the axial XXZ model. The thermodynamics of the Ising chain for s 1/2 is shown to be equivalent to that of a system of two species of solitons and for s = 1 to that of a system of six species of soliton pairs. Solitons exist on single bonds but soliton pairs may be spread across many bonds. The thermodynamics of a system of domains spanning up to M lattice sites is amenable to exact analysis and shown to become equivalent, in the limit M → ∞, to the thermodynamics of the s = 1/2 Ising chain. A relation is presented between the solitons in the Ising limit and the spinons in the XX limit of the s = 1/2 XXZ chain. The exclusion statistics is semionic for both spinons and solitons but the spinon vacuum is unique whereas the soliton vacuum is twofold with broken symmetry.

Indexing (details)


Subject
Theoretical physics
Classification
0753: Theoretical physics
Identifier / keyword
Pure sciences; Axial exchange; Quantum spin chains; Quasiparticles
Title
Quasiparticles in quantum spin chains with strong axial exchange anisotropy
Author
Lu, Ping
Number of pages
135
Publication year
2009
Degree date
2009
School code
0186
Source
DAI-B 70/07, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781109288988
Advisor
Muller, Gerhard
University/institution
University of Rhode Island
University location
United States -- Rhode Island
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3367997
ProQuest document ID
304986086
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304986086
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