From the Bethe Ansatz to the Gessel-Viennot Theorem
Combinatorics
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
We state and prove several theorems that demonstrate how the coordinate Bethe Ansatz for the eigenvectors of suitable transfer matrices of a generalised inhomogeneous five-vertex model on the square lattice, given certain conditions hold, is equivalent to the Gessel-Viennot determinant for the number of configurations of non-intersecting directed lattice paths, or vicious walkers, with various boundary conditions. Our theorems are sufficiently general to allow generalisation to any regular planar lattice.
Keywords
Cite
@article{arxiv.math/0006153,
title = {From the Bethe Ansatz to the Gessel-Viennot Theorem},
author = {R. Brak and J. W. Essam and A. L. Owczarek},
journal= {arXiv preprint arXiv:math/0006153},
year = {2007}
}