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EPSRC Reference: GR/M97497/01
Title: ALGEBRAIC APPROACHES TO SOLVABLE LATTICE MODELS
Principal Investigator: Weston, Dr R
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: S of Mathematical and Computer Sciences
Organisation: Heriot-Watt University
Scheme: Standard Research (Pre-FEC)
Starts: 01 September 2000 Ends: 31 August 2003 Value (£): 127,919
EPSRC Research Topic Classifications:
Mathematical Physics
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:  
Summary on Grant Application Form
The proposed work considers two algebraic approaches to solvable lattice models. The first is the vertex operator approach. This will be applied to RSOS and dilute-bond ABF models. The main task is to construct mathematical and physical pictures of the analogue of conformal field theory primary operators. The primary mathematical definition of these q-primary operators will be via a coset construction, the physical construction in terms of half-infinite lattice insertions. We will use these operators to compute impurity correlation functions. The second approach is a new variant of the Bethe Ansatz. In this method a change of basis is defined in terms of a certain twisting operation. The result is that the relation between a local spin operator and the components of the monodromy matrix is greatly simplified, as is the calculation of correlation functions. We will develop and extend the method, and apply it to compute correlation functions and form-factors for the infinite-volume XXZ model. Using the understanding we have gained, we will then construct a correspondence with the vertex operator approach. Finally, we shall find the appropriate twist for he 8-vertex and ABF models and use the method to compute finite-volume correlation functions for these models.
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Organisation Website: http://www.hw.ac.uk