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

摘要

We study the magnetic field dependence of the entanglement entropy in quantumphase transition induced by a quench of the XX, XXX and the LMG model. Theentropy for a block of $L$ spins with the rest follows a logarithmic scalinglaw where the block size $L$ is restricted due to the dependence of theprefactor on the quench time. Within this restricted region the entropyundergoes a renormalization group (RG) flow. From the RG flow equation we haveanalytically determined the magnetic field dependence of the entropy. Theanisotropy parameter dependence of the entropy for the XY and the LMG model hasalso been studied in this framework. The results are found to be in excellentagreement with that obtained by other authors from numerical studies withoutany quench.