Impurity spin relaxation in S=1/2 XX chains

Dynamic autocorrelations (S-i(a)(t)S-i(a)) (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 tb Fermi operators; the effects of finite system size can be eliminated. Two distinct temperature regimes are observed in the long-time asymptotic behavior of the bulk correlations. 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 ultimately follow power laws at all T, with intermediate exponential phases at high T. The power laws for the z correlation and the boundary correlations can be derived from the impurity-induced changes in the properties of the Jordan-Wigner fernion states.