Numerical evaluation of convex-roof entanglement measures with applications to spin rings

TL;DR

This paper introduces two numerical algorithms for evaluating convex-roof entanglement measures, demonstrating their effectiveness through tests and applying them to analyze entanglement in finite-temperature spin ring systems.

Contribution

The paper presents novel numerical algorithms for convex-roof entanglement measures and applies them to study entanglement in spin rings at finite temperature.

Findings

Algorithms show good convergence properties.

Highly entangled states are achievable at low temperatures.

Optimal magnetic field tuning enhances entanglement.

Abstract

We present two ready-to-use numerical algorithms to evaluate convex-roof extensions of arbitrary pure-state entanglement monotones. Their implementation leaves the user merely with the task of calculating derivatives of the respective pure-state measure. We provide numerical tests of the algorithms and demonstrate their good convergence properties. We further employ them in order to investigate the entanglement in particular few-spins systems at finite temperature. Namely, we consider ferromagnetic Heisenberg exchange-coupled spin-1/2 rings subject to an inhomogeneous in-plane field geometry obeying full rotational symmetry around the axis perpendicular to the ring through its center. We demonstrate that highly entangled states can be obtained in these systems at sufficiently low temperatures and by tuning the strength of a magnetic field configuration to an optimal value which is identified numerically.