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

N. CANOSA; J.M. MATERA; R. ROSSIGNOLI

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

The American Physical Society

Lugar: NY; Año: 2007 vol. 76 p. 223101 - 223109

1050-2947

We discuss the application of the static path plus random phase approximation(SPA+RPA) and the ensuing mean field+RPA treatment to the evaluation ofentanglement in composite systems at finite temperature. These methods involvejust local diagonalizations and the determination of the generalized collectivevibrational frequencies. As illustration, we evaluate the pairwise entanglementin a fully connected XXZ chain of $n$ spins at finite temperature in atransverse magnetic field $b$. It is shown that already the mean field+RPAprovides an accurate analytic description of the concurrence below the meanfield critical region ($|b|<b_c$), exact for large $n$, whereas the full SPA+RPAis able to improve results for finite systems in the critical region. It isalso demonstrated that for $T>0$ weak entanglement also arises when the groundstate is separable ($|b|>b_c$), with the limit temperature for pairwiseentanglement exhibiting quite distinct regimes for $|b|<b_c$ and $|b|>b_c$.