XXZ scalar products and KP

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

References in corpus (6)

• Separation of Variables. New Trends.
• Supersymmetric vacua and Bethe ansatz
• Quantum integrability and supersymmetric vacua
• Temperature Correlations of Quantum Spins
• Temperature Correlation of Quantum Spins
• Domain wall partition functions and KP

Cited by in corpus (14)

• Classical tau-function for quantum spin chains
• Vertex models, TASEP and Grothendieck polynomials
• An Izergin-Korepin procedure for calculating scalar products in six-vertex models
• Inner products of Bethe states as partial domain wall partition functions
• Three-point function of semiclassical states at weak coupling
• KP and Toda tau functions in Bethe ansatz
• Variations on Slavnov's scalar product
• Phase model expectation values and the 2-Toda hierarchy
• Free fermions in classical and quantum integrable models
• Studies in Integrable Quantum Lattice Models and Classical Hierarchies
• The monodromy matrix in the F-basis for arbitrary six-vertex models
• Correlation functions of charged free boson and fermion systems
• $Q$-Boson model and relations with integrable hierarchies
• Comments on Slavnov products, Temperley-Lieb open spin chains, and KP tau functions