XXZ scalar products and KP
arXiv:0903.2611 · doi:10.1016/j.nuclphysb.2009.04.019
Abstract
Using a Jacobi-Trudi-type identity, we show that the scalar product of a general state and a Bethe eigenstate in a finite-length XXZ spin-1/2 chain is (a restriction of) a KP tau function. This leads to a correspondence between the eigenstates and points on Sato's Grassmannian. Each of these points is a function of the rapidities of the corresponding eigenstate, the inhomogeneity variables of the spin chain and the crossing parameter.
14 pages, LaTeX2E