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

TL;DR

This paper investigates how magnetic fields influence entanglement entropy during quantum phase transitions in one-dimensional spin models, revealing a logarithmic scaling law and RG flow behavior under quenched conditions.

Contribution

It provides an analytical description of the magnetic field dependence of entanglement entropy in quenched spin systems, extending understanding beyond numerical results.

Findings

Entropy follows a logarithmic scaling law with block size.

The prefactor of the entropy depends on quench time and magnetic field.

Analytical results agree with previous numerical studies.

Abstract

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.