  An analytic method is proposed to compute the surface energy and elementary
excitations of the XXZ spin chain with generic non-diagonal boundary fields.
For the gapped case, in some boundary parameter regimes the contributions of
the two boundary fields to the surface energy are non-additive. Such a
correlation effect between the two boundaries also depends on the parity of the
site number $N$ even in the thermodynamic limit $N\to\infty$. For the gapless
case, contributions of the two boundary fields to the surface energy are
additive due to the absence of long-range correlation in the bulk. Although the
$U(1)$ symmetry of the system is broken, exact spinon-like excitations, which
obviously do not carry spin-$\frac12$, are observed. The present method
provides an universal procedure to deal with quantum integrable systems either
with or without $U(1)$ symmetry.
