Impurity spin relaxation in S=1/2 XX chains

Details Impurity spin relaxation in S=1/2 XX chains Impurity spin relaxation in S=1/2 XX chains

1999-05-20

arxiv.org/abs/cond-mat/9905293v2

Phys. Rev. B 61, 4026-4032 (2000) (1 Feb)

Physics

Condensed Matter

Statistical Mechanics

Final version to be published in Phys. Rev. B. Three references added, extended discussion of relation to previous work

Scientific paper

10.1103/PhysRevB.61.4026

Dynamic autocorrelations $$ (\alpha=x,z) of an isolated impurity spin in a S=1/2 XX chain are calculated. The impurity spin, defined by a local change in the nearest-neighbor coupling, is either in the bulk or at the boundary of the open-ended chain. The exact numerical calculation of the correlations employs the Jordan-Wigner mapping from spin operators to Fermi operators; effects of finite system size can be eliminated. Two distinct temperature regimes are observed in the long-time asymptotic behavior. At T=0 only power laws are present. At high T the x correlation decays exponentially (except at short times) while the z correlation still shows an asymptotic power law (different from the one at T=0) after an intermediate exponential phase. The boundary impurity correlations follow power laws at all T. The power laws for the z correlation and the boundary correlations can be deduced from the impurity-induced changes in the properties of the Jordan-Wigner fermion states.

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