Correlation functions of the openXXZchain: I

Abstract

We consider the XXZ spin chain with diagonal boundary conditions in the framework of algebraic Bethe Ansatz. Using the explicit computation of the scalar products of Bethe states and a revisited version of the bulk inverse problem, we calculate the elementary building blocks for the correlation functions. In the limit of half-infinite chain, they are obtained as multiple integrals of usual functions, similar to the case of periodic boundary conditions.

Drinfeld twists of the open XXZ chain with non-diagonal boundary terms

“…A similar situation already appeared in the open XXZ chain with diagonal K-matrices [11,12]. However, such polarization free forms of the pseudo-particle creation operators are crucial for computing partition functions and scalar products [4,10,9,12,34].…”

“…It is very convenient to introduce a vector λ ∈ V associated with the boundary parameters {λ i }, 12) where {ǫ i , i = 1, 2} form the orthonormal basis of V such that ǫ i , ǫ j = δ ij .…”

Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms

“…It was shown that in order to compute correlation functions of the closed XXZ chain [2] and the open XXZ chain with diagonal boundary terms [17,18], one suffices to calculate the scalar products of an on-shell Bethe state and a general state (an off-shell Bethe state). The aim of this paper is to give the explicit expressions of the following scalar products of the open XXZ chain with non-diagonal boundary terms:…”

A bispectral q-hypergeometric basis for a class of quantum integrable models

“…It appears that an explicit characterization of the Hamiltonian's eigenfunctions as polynomials offers the possibility of studying the correspondence between Bethe roots and solutions of algebraic equations [101]. On the other hand, in the thermodynamic limit, either from the algebraic Bethe ansatz setting [103] or the q−vertex operator approach [104,85], correlation functions and form factors are always given in terms of multiple integral representations. Although formally satisfying, these are difficult objects to handle for practical applications.…”