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

Understand

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.