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

N. CANOSA; M. MATERA; R. ROSSIGNOLI

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

APS

Lugar: New York; 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 quantum systems at finite temperature. These methodsinvolve just local diagonalizations and the determination of the generalizedcollective vibrational frequencies. As illustration, we evaluate the pairwiseentanglement in a fully connected XXZ chain of  n spins at finite temperaturein a transverse 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 fullSPA+RPA is able to improve results for finite systems in the critical region.It is proven as well that for T>0 weak entanglement also arises when theground state is separable (|b|>b_c), with the limit temperature for pairwiseentanglement exhibiting quite distinct regimes for |b|<b_c and |b|>b_c.