XXZ scalar products and KP
O Foda, M Wheeler, M Zuparic
NUCLEAR PHYSICS B | ELSEVIER SCIENCE BV | Published : 2009
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-frac(1, 2) chain is (a restriction of) a KP τ 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. © 2009 Elsevier B.V. All rights reserved.
We wish to thank Professors M. Jimbo, N. Kitanine, V.E. Korepin, E. Mukhin, T. Shiota and K. Takasaki for useful remarks on this work and on related topics. M.W. and M.Z. are supported by Australian Postgraduate Awards and by the Department of Mathematics and Statistics, The University of Melbourne.