Correlation functions of the half-infinite XXZ spin chain with a triangular boundary

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 $\langle \sigma_1^a\rangle$ with $a=z,\pm$ are obtained. Exploiting the spin-reversal property, relations between $n$-fold integrals of elliptic theta functions are extracted.