Correlation functions of the half-infinite XXZ spin chain with a triangular boundary
P. Baseilhac (Laboratoire de Mathématiques et Physique Théorique CNRS/UMR 7350, Fédération Denis Poisson FR2964, Université de Tours, Parc de Grammont, Tours, 37200, France); T. Kojima (Department of Mathematics and Physics, Faculty of Engineering, Yamagata University, Jonan 4-3-16, Yonezawa, 992-8510, Japan)
The half-infinite XXZ spin chain with a triangular boundary is considered in the massive regime. Two integral representations of correlation functions are proposed using bosonization. Sufficient conditions such that the expressions for triangular boundary conditions coincide with those for diagonal boundary conditions are identified. As an application, summation formulae of the boundary expectation values 〈σ1a〉 with a=z,± are obtained. Exploiting the spin-reversal property, relations between n -fold integrals of elliptic theta functions are extracted.
