Renormalization of concurrence: the application of quantum renormalization group to the quantum information systems

TL;DR

This paper applies quantum renormalization group techniques to analyze how entanglement, measured by concurrence, scales in many-body quantum systems, revealing critical behavior at phase transitions.

Contribution

It introduces a method to compute entanglement scaling using renormalization group, linking quantum information measures with critical phenomena in many-body systems.

Findings

Concurrence scales with system size and diverges at critical points.

Derivative of concurrence diverges with a critical exponent.

Renormalization group approach effectively captures quantum entanglement behavior.

Abstract

We have combined the idea of renormalization group and quantum information theory. We have shown how the entanglement or concurrence evolve as the size of the system being large, i.e. the finite size scaling is obtained. Moreover, It introduces how the renormalization group approach can be implemented to obtain the quantum information properties of a many body system. We have obtained the concurrence as a measure of entanglement, its derivatives and their scaling behavior versus the size of system for the one dimensional Ising model in transverse field. We have found that the derivative of concurrence between two blocks each containing half of the system size diverges at the critical point with the exponent which is directly associated with the divergence of the correlation length.