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

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

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

AMER PHYSICAL SOC

Año: 2007 vol. 76 p. 22310 - 22310

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 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 an 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∣<bc), exact for large n, whereas the full SPA+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 the ground state is separable (∣b∣>bc), with the limit temperature for pairwise entanglement exhibiting quite distinct regimes for ∣b∣<bc and ∣b∣>bc.