Shou-Shu Gong and Gang Su *
College of Physical Sciences, Graduate University of Chinese Academy of Sciences, P.O. Box 4588, Beijing 100049,
People’s Republic of China
(Received 16 April 2009; published 20 July 2009)

Abstract:

The thermal pairwise entanglement (TE) of the S=1/2 XY chain in a transverse magnetic field is exactly resolved by means of the Jordan-Wigner transformation in the thermodynamic limit N→∞. It is found that the TE vanishes at a fixed point with temperature Tc ≈0.4843J, which is independent of the magnetic field. A thermal quantity is proposed to witness the entangled state. Furthermore, the TE of the S=1/2 antiferromagnetic-ferromagnetic (AF-F) Heisenberg chain is studied by the transfer-matrix renormalization-group method. The TEs of the spins coupled by AF and F interactions are found to behave distinctively. The vanishing temperature of the field-induced TE of the spins coupled by F interactions is observed dependent on the magnetic field. The results are further confirmed and analyzed within a mean-field framework.