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XXZ scalar products and KP

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arxiv 0903.2611 v1 pith:XLGNUTQ7 submitted 2009-03-16 math-ph math.MP

O Foda , M Wheeler , M Zuparic This is my paper
classification math-phmath.MP
keywords chaineigenstatefunctionpointsscalarbethecorrespondencecorresponding
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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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  1. More on Slavnov Products of Spin Chains and KP Hierarchy Tau Functions

    hep-th 2025-05 reject novelty 5.0 of 10

    Slavnov products of Bethe states in rational spin chains are shown to be KP tau functions, with new Wronskian and Baker-Akhiezer formulas, but the key identification relies on an unverified assumption.

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