  A relation between geometric phases and criticality of spin chains are
studied by using the quantum renormalization-group approach. We have shown how
the geometric phase evolve as the size of the system becomes large, i.e., the
finite size scaling is obtained. The renormalization scheme demonstrates how
the first derivative of the geometric phase with respect to the field strength
diverges at the critical point and maximum value of the first derivative and
its position scales with an exponent of the system size. This exponent is
directly associated with the critical properties of the model where, the
exponent governing the divergence of the correlation length close to the
quantum critical point.
