School Seminars and Colloquia

Finite size lattice results for the two-boundary Temperley-Lieb loop model

Completion Seminar

by Anita Ponsaing


Institution: The Department of Mathematics and Statistics, The University of Melbourne
Date: Tue 14th June 2011
Time: 12:00 PM
Location: Russell Love Theatre, The Richard Berry Building, The University of Melbourne

Abstract: The integrable Temperley-Lieb loop (TL(n)) model is central in the field of integrable lattice models. It is closely related to the quantum XXZ spin chain, and at n=1 it also corresponds to the bond percolation problem on a square lattice. For this value of n the model possesses some additional symmetry properties. We will discuss the TL(n=1) model on a lattice strip with two non-trivial boundaries.

In particular we describe the calculation of certain components of the transfer matrix ground-state eigenvector, as well as its normalisation.
We also present the exact calculation of a boundary-to-boundary correlation function for finite lattice sizes. All of these calculations rely on recursions and symmetries satisfied by the transfer matrix, and the final results are given in terms of a polynomial character of the symplectic group.

The final part of the talk describes a separation of variables method for this symplectic character, which will hopefully be useful in calculating the asymptotic limit of our results as the system size becomes large. This will allow us to compare our exact results with non-rigorous conformal field theoretic results that have been previously calculated.

For More Information: Contact: Jan de Gier. Email: jdgier@unimelb.edu.au