The Ladder Operator Approach to Constructing Conserved Operators in Integrable One-Dimensional Lattice Models

Takizawa, M. C. (2005). The Ladder Operator Approach to Constructing Conserved Operators in Integrable One-Dimensional Lattice Models PhD Thesis, School of Physical Sciences, The University of Queensland.

       
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Author Takizawa, M. C.
Thesis Title The Ladder Operator Approach to Constructing Conserved Operators in Integrable One-Dimensional Lattice Models
School, Centre or Institute School of Physical Sciences
Institution The University of Queensland
Publication date 2005
Thesis type PhD Thesis
Supervisor Links, Jon
Gould, Mark
Total pages 152
Collection year 2005
Language eng
Subjects L
230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
780101 Mathematical sciences
Formatted abstract

The theory of constructing integrable systems using solutions to the Yang-Baxter equation (YBE) is well established. The conserved operators can be obtained by a series expansion for the family of commuting transfer matrices. Another approach is to use the ladder operator, which permits a recursive method through repeated commutators, to obtain the conserved operators. The ladder operator for models where the solution of the YBE has the difference property is well known.

 

Recently it has been shown that a ladder operator exists for the Hubbard model, which does not have the difference property, and the present work extends this to a general theory for the construction of the ladder operator for any integrable system obtained through the YBE, with the XYh model as an example. The existence of ladder operators for integrable models constructed from other variants of the YBE, such as closed chains with quantum algebra symmetry and the Heisenberg model with single site impurity, is also considered.

Keyword Lattice theory
Mathematical physics

 
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Created: Fri, 24 Aug 2007, 18:45:04 EST