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The thermodynamic properties of the XXZ spin chain with integrable openboundary conditions at the gaped region (i.e., the anisotropic parameter $\eta$being a real number) are investigated.It is shown that the contribution of theinhomogeneous term in the $T-Q$ relation of the ground state and elementaryexcited state can be neglected when the size of the system $N$ tends toinfinity. The surface energy and elementary excitations induced by theunparallel boundary magnetic fields are obtained.

Surface energy and elementary excitations of the XXZ spin chain with arbitrary boundary fields