Thermal entanglement in one-dimensional Heisenberg quantum spin chains under magnetic fields

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{yields}{infinity}. It is found that the TE vanishes at a fixed point with temperature T{sub c}{approx_equal}0.484...

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Veröffentlicht in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2009-07, Vol.80 (1), Article 012323
Hauptverfasser: Gong, Shou-Shu, Su, Gang
Format: Artikel
Sprache:eng
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Zusammenfassung: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{yields}{infinity}. It is found that the TE vanishes at a fixed point with temperature T{sub c}{approx_equal}0.484 3J, 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.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.80.012323