Scaling of entanglement between separated blocks in spin chains at criticality

TL;DR

This paper analyzes how entanglement between separated blocks in spin chains behaves at criticality, revealing a universal scaling law that interpolates between individual spins and larger blocks, and relates to correlation functions.

Contribution

It introduces a universal scaling form for entanglement between separated blocks at criticality, linking it to correlation functions and invariance under scale transformations.

Findings

Entanglement scales as a product of power law and exponential decay.

Entanglement is invariant under simultaneous scale transformations.

The study estimates entanglement between separated regions in quantum fields.

Abstract

We compute the entanglement between separated blocks in certain spin models showing that at criticality this entanglement is a function of the ratio of the separation to the length of the blocks and can be written as a product of a power law and an exponential decay. It thereby interpolates between the entanglement of individual spins and blocks of spins. It captures features of correlation functions at criticality as well as the monogamous nature of entanglement. We exemplify invariant features of this entanglement to microscopic changes within the same universality class. We find this entanglement to be invariant with respect to simultaneous scale transformations of the separation and the length of the blocks. As a corollary, this study estimates the entanglement between separated regions of those quantum fields to which the considered spin models map at criticality.