The renormalization of entanglement in the anisotropic Heisenberg (XXZ) model

TL;DR

This paper investigates how entanglement measures like concurrence and entanglement entropy behave under renormalization in the anisotropic Heisenberg (XXZ) model, revealing critical properties and phase distinctions through nonanalytic behaviors.

Contribution

The study applies a renormalization approach to analyze entanglement in the XXZ model, linking entanglement scaling to quantum critical phenomena and introducing a quantum group-based method for deeper insight.

Findings

Entanglement measures saturate in different phases.

Nonanalytic behavior signals quantum critical points.

Scaling exponents relate to correlation length divergence.

Abstract

We have applied our recent approach (Kargarian, et.al Phys. Rev. A 76, 60304 (R) (2007)) to study the quantum information properties of the anisotropic s=1/2 Heisenberg chain. We have investigated the underlying quantum information properties like the evolution of concurrence, entanglement entropy, nonanalytic behaviours and the scaling close to the quantum critical point of the model. Both the concurrence and the entanglement entropy develop two saturated values after enough iterations of the renormalization of coupling constants. This values are associated with the two different phases, i.e Neel and spin liquid phases. The nonanalytic behaviour comes from the divergence of the first derivative of both measures of entanglement as the size of system becomes large. The renormalization scheme demonstrates how the minimum value of the first derivative and its position scales with an exponent of the system size. It is shown that this exponent is directly related to the critical properties of the model, i.e. the exponent governing the divergence of the correlation length close to the quantum critical point. We also use a renormalization method based on the quantum group concept in order to get more insight about the critical properties of the model and the renormalization of entanglement.