TL;DR
This paper demonstrates that scalar products in the XXZ spin chain can be expressed as KP tau functions, establishing a link between eigenstates and points on Sato's Grassmannian, with implications for integrable systems.
Contribution
It introduces a Jacobi-Trudi-type identity to connect XXZ scalar products with KP tau functions, revealing a geometric correspondence with Sato's Grassmannian.
Findings
Scalar products are shown to be KP tau functions.
Eigenstates correspond to points on Sato's Grassmannian.
The correspondence depends on rapidities, inhomogeneity variables, and the crossing parameter.
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.
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