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

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{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.

Authors:
;  [1]
  1. College of Physical Sciences, Graduate University of Chinese Academy of Sciences, P.O. Box 4588, Beijing 100049 (China)
Publication Date:
OSTI Identifier:
21313233
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 80; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.80.012323; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANTIFERROMAGNETISM; FERROMAGNETISM; HEISENBERG MODEL; MAGNETIC FIELDS; MATRICES; MEAN-FIELD THEORY; ONE-DIMENSIONAL CALCULATIONS; QUANTUM ENTANGLEMENT; RENORMALIZATION; SPIN; TRANSFORMATIONS

Citation Formats

Shoushu, Gong, and Gang, Su. Thermal entanglement in one-dimensional Heisenberg quantum spin chains under magnetic fields. United States: N. p., 2009. Web. doi:10.1103/PHYSREVA.80.012323.
Shoushu, Gong, & Gang, Su. Thermal entanglement in one-dimensional Heisenberg quantum spin chains under magnetic fields. United States. https://doi.org/10.1103/PHYSREVA.80.012323
Shoushu, Gong, and Gang, Su. 2009. "Thermal entanglement in one-dimensional Heisenberg quantum spin chains under magnetic fields". United States. https://doi.org/10.1103/PHYSREVA.80.012323.
@article{osti_21313233,
title = {Thermal entanglement in one-dimensional Heisenberg quantum spin chains under magnetic fields},
author = {Shoushu, Gong and Gang, Su},
abstractNote = {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.},
doi = {10.1103/PHYSREVA.80.012323},
url = {https://www.osti.gov/biblio/21313233}, journal = {Physical Review. A},
issn = {1050-2947},
number = 1,
volume = 80,
place = {United States},
year = {Wed Jul 15 00:00:00 EDT 2009},
month = {Wed Jul 15 00:00:00 EDT 2009}
}