Description of thermal entanglement with the static path plus random-phase approximation

TL;DR

This paper applies the SPA+RPA method to analyze thermal entanglement in quantum spin systems, showing that it accurately describes pairwise entanglement at finite temperature and near critical points, with improvements over mean field approaches.

Contribution

It demonstrates the effectiveness of SPA+RPA in evaluating thermal entanglement in quantum spin chains, especially near critical regions and for finite systems.

Findings

Mean field+RPA accurately describes entanglement below the critical field for large systems.

SPA+RPA improves results for finite systems in the critical region.

Weak entanglement can occur at finite temperature even when the ground state is separable.

Abstract

We discuss the application of the static path plus random phase approximation (SPA+RPA) and the ensuing mean field+RPA treatment to the evaluation of entanglement in composite quantum systems at finite temperature. These methods involve just local diagonalizations and the determination of the generalized collective vibrational frequencies. As illustration, we evaluate the pairwise entanglement in a fully connected XXZ chain of $n$ spins at finite temperature in a transverse magnetic field $b$. It is shown that already the mean field+RPA provides an accurate analytic description of the concurrence below the mean field critical region ($|b|<b_c$), exact for large $n$, whereas the full SPA+RPA is able to improve results for finite systems in the critical region. It is proved as well that for $T>0$ weak entanglement also arises when the ground state is separable ($|b|>b_c$), with the limit temperature for pairwise entanglement exhibiting quite distinct regimes for $|b|<b_c$ and $|b|>b_c$.