  We study the magnetic field dependence of the entanglement entropy in quantum
phase transition induced by a quench of the XX, XXX and the LMG model. The
entropy for a block of $L$ spins with the rest follows a logarithmic scaling
law where the block size $L$ is restricted due to the dependence of the
prefactor on the quench time. Within this restricted region the entropy
undergoes a renormalization group (RG) flow. From the RG flow equation we have
analytically determined the magnetic field dependence of the entropy. The
anisotropy parameter dependence of the entropy for the XY and the LMG model has
also been studied in this framework. The results are found to be in excellent
agreement with that obtained by other authors from numerical studies without
any quench.
