Abstract
Starting from the T-Q equation of an open integrable \( {\text{spin}} - \frac{1}{2} \) XXZ quantum spin chain with nondiagonal boundary terms, we derive a nonlinear integral equation (NLIE) of the sine-Gordon model on a finite interval. We compute the boundary energy and the Casimir energy for the sine-Gordon model with both left and right boundaries. A relation between the boundary parameters of the continuum model and the lattice model is given. We also present numerical results for the effective central charge of an open \( {\text{spin}} - \frac{1}{2} \) XXZ quantum spin chain which find agreement with our analytical result for the central charge of the sine-Gordon model in the ultraviolet (UV) limit.
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