Low energy states dynamic of entanglement for spin systems

TL;DR

This paper explores how the dynamic behavior of entanglement in low energy states of one-dimensional spin systems reveals quantum phase transitions and scaling laws near critical points, combining quantum renormalization group ideas.

Contribution

It introduces a method to analyze the evolution of entanglement in low energy states near quantum critical points using quantum renormalization group concepts.

Findings

Derivative of entanglement maximum timing diverges at critical point

Scaling behavior of entanglement dynamics matches static ground state

Entanglement evolution signals quantum phase transition

Abstract

We have composed the ideas of quantum renormalization group and quantum information by exploring the low energy states dynamic of entanglement resources of a system close to its quantum critical point. We demonstrate the low energy states dynamical quantities of the one dimensional magnetic systems could show the quantum phase transition point and shows the scaling behavior in the vicinity of the transition point. To present our idea, we study the evolution of two spins entanglement in the one-dimensional Ising model in the transverse field. The system is initialized as the so-called thermal ground state of the pure Ising model. We investigate evolvement of the generation of entanglement with increasing the magnetic field. We have obtained that the derivative of the time at which the entanglement reaches its maximums with respect to the transverse field, diverges at the critical point and its scaling behaviors versus the size of the system are as same as the static ground state entanglement of the the system.