  We embody the density matrix renormalization group method for the 19-vertex
model on a square lattice; the 19-vertex model is regarded to be equivalent to
the XY model for small interaction. The transfer matrix of the 19-vertex model
is classified by the total number of arrows incoming into one layer of the
lattice. By using this property, we reduce the dimension of the transfer matrix
appearing in the density matrix renormalizaion group method and obtain a very
nice value of the conformal anomaly which is consistent with the value at the
Berezinskii-Kosterlitz-Thouless transition point.
  Keyword : Kosterlitz-Thouless, Renormalization group
