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Magnetic field dependence of the entanglement entropy of one dimensional spin systems in quantum phase transition induced by a quench

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.