  We present a novel real-space renormalization group(RG) for the
one-dimensional XXZ model in the critical regime, reconsidering the role of the
cut-off parameter in Wilson's RG for the Kondo impurity problem. We then
demonstrate the RG calculation for the XXZ chain with the free boundary.
Comparing the hierarchical structure of the obtained low-energy spectrum with
the Bethe ansatz result, we find that the proper scaling dimension is
reproduced as a fixed point of the RG transformation.
