Inner products of Bethe states as partial domain wall partition functions
High Energy Physics - Theory
2015-06-05 v3 Mathematical Physics
math.MP
Abstract
We study the inner product of Bethe states in the inhomogeneous periodic XXX spin-1/2 chain of length L, which is given by the Slavnov determinant formula. We show that the inner product of an on-shell M-magnon state with a generic M-magnon state is given by the same expression as the inner product of a 2M-magnon state with a vacuum descendent. The second inner product is proportional to the partition function of the six-vertex model on a rectangular Lx2M grid, with partial domain-wall boundary conditions.
Keywords
Cite
@article{arxiv.1207.2562,
title = {Inner products of Bethe states as partial domain wall partition functions},
author = {Ivan Kostov and Yutaka Matsuo},
journal= {arXiv preprint arXiv:1207.2562},
year = {2015}
}
Comments
14 pages, 6 figures, typos corrected and a reference added