Stretched exponential-like impurity relaxation in the S=1/2 XY chain: a numerical study

We use the continued fraction formalism to show that a weakly bound, S=1/2, impurity spin, in a S=1/2 XY chain exhibits slow relaxation. The dynamical xx-correlation of the impurity spin, at different couplings to the rest of the chain, is best described by a non-universal stretched-exponential-like (SEL) decay at large times. The zz-correlation for that spin shows exponential-like decay. The host spins relax faster than the impurity spin. To our knowledge, this is the first study which introduces a simple 1D spin Hamiltonian and solves the Heisenberg equation of motion for the impurity spin to obtain SEL relaxation.