Entanglement and quantum state geometry of spin system with all-range Ising-type interaction

TL;DR

This paper investigates how entanglement in a spin-1/2 system with all-range Ising interactions depends on system size and initial conditions, exploring the geometric structure of entangled states and their relation to manifold curvature.

Contribution

It introduces a geometric framework linking entanglement properties to the scalar curvature of the state manifold in an all-range Ising spin system.

Findings

Entanglement varies with the number of spins and initial states.

The geometry of entangled states is characterized by a specific manifold.

Entanglement correlates with the scalar curvature of the state manifold.

Abstract

The evolution of $N$ spin-$1/2$ system with all-range Ising-type interaction is considered. For this system we study the entanglement of one spin with the rest spins. It is shown that the entanglement depends on the amount of spins and the initial state. Also the geometry of manifold which contains entangled states is obtained. Finally we find the dependence of entanglement on the scalar curvature of manifold and examine it for different number of spins in the system.