%0 Book Section %1 statphys23_0577 %A Rossignoli, R. %A Canosa, N. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K chains entanglement finite heisenberg quantum spin statphys23 temperature topic-8 %T Entanglement in Heisenberg spin chains at finite temperature %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=577 %X We discuss some aspects of quantum entanglement in finite cyclic spin chains at finite temperature interacting through Heisenberg couplings in the presence of a transverse magnetic field. We first examine the global entanglement through the evaluation of the negativity associated with partitions of the whole system and subsystems 1. The negativity is a computable approximate measure of bipartite entanglement apt for mixed states. Limit temperatures for non-zero global negativities are shown to be strictly independent of the uniform field in $XXZ$ type models, in spite of the quantum transitions these models may exhibit at $T=0$, while in anisotropic XYZ models they tend to increase for large fields, being always higher than those limiting pairwise entanglement. Special reentry effects for $T>0$ are also discussed. We next examine the pairwise entanglement at finite temperature in chains with nearest neighbor $XX$ type coupling, by means of exact results obtained through the Jordan-Wigner transformation plus number parity projected statistics 2. It is shown that while at $T=0$ there is always entanglement between any two spins in a narrow field interval just before the transition to the aligned state, at sufficiently low but non-zero temperatures entanglement remains non-zero for arbitrarily high fields, for any pair separation $L$, although its magnitude decreases exponentially with the field. The corresponding limit temperatures are as well analyzed. Other related features currently under investigation will also be discussed. \\ 1) R. Rossignoli, N. Canosa, Phys. Rev. A 72, 012335 (2005); A 73, 022347 (2006). \\ 2) N. Canosa, R. Rossignoli, Phys. Rev. A 75 (2007, in press)

@incollection{statphys23_0577, abstract = {We discuss some aspects of quantum entanglement in finite cyclic spin chains at finite temperature interacting through Heisenberg couplings in the presence of a transverse magnetic field. We first examine the global entanglement through the evaluation of the negativity associated with partitions of the whole system and subsystems [1]. The negativity is a computable approximate measure of bipartite entanglement apt for mixed states. Limit temperatures for non-zero global negativities are shown to be strictly independent of the uniform field in $XXZ$ type models, in spite of the quantum transitions these models may exhibit at $T=0$, while in anisotropic XYZ models they tend to increase for large fields, being always higher than those limiting pairwise entanglement. Special reentry effects for $T>0$ are also discussed. We next examine the pairwise entanglement at finite temperature in chains with nearest neighbor $XX$ type coupling, by means of exact results obtained through the Jordan-Wigner transformation plus number parity projected statistics [2]. It is shown that while at $T=0$ there is always entanglement between any two spins in a narrow field interval just before the transition to the aligned state, at sufficiently low but non-zero temperatures entanglement remains non-zero for arbitrarily high fields, for any pair separation $L$, although its magnitude decreases exponentially with the field. The corresponding limit temperatures are as well analyzed. Other related features currently under investigation will also be discussed. \\ 1) R. Rossignoli, N. Canosa, Phys. Rev. A 72, 012335 (2005); A 73, 022347 (2006). \\ 2) N. Canosa, R. Rossignoli, Phys. Rev. A 75 (2007, in press)}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Rossignoli, R. and Canosa, N.}, biburl = {https://www.bibsonomy.org/bibtex/23abec7c55bf792cc35303b822e3a265a/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {8dab9a882ed161f9007d47847a95f90b}, intrahash = {3abec7c55bf792cc35303b822e3a265a}, keywords = {chains entanglement finite heisenberg quantum spin statphys23 temperature topic-8}, month = {9-13 July}, timestamp = {2007-06-20T10:16:24.000+0200}, title = {Entanglement in Heisenberg spin chains at finite temperature}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=577}, year = 2007 }