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Long-Time Tails and Anomalous Slowing Down in the Relaxation of Spatially Inhomogeneous Excitations in Quantum Spin Chains

By G. O. Berim, S. Berim and G. G. Cabrera

Abstract

Exact analytic calculations in spin-1/2 XY chains, show the presence of longtime tails in the asymptotic dynamics of spatially inhomogeneous excitations. The decay of inhomogeneities, for t → ∞, is given in the form of a power law (t/τQ) −νQ where the relaxation time τQ and the exponent νQ depend on the wave vector Q, characterizing the spatial modulation of the initial excitation. We consider several variants of the XY model (dimerized, with staggered magnetic field, with bond alternation, and with isotropic and uniform interactions), that are grouped into two families, whether the energy spectrum has a gap or not. Once the initial condition is given, the non-equilibrium problem for the magnetization is solved in closed form, without any other assumption. The long-time behavior for t → ∞ can be obtained systematically in a form of an asymptotic series through the stationary phase method. We found that gapped models show critical behavior with respect to Q, in the sense that there exist critical values Qc, where the relaxation time τQ diverges and the exponent νQ changes discontinuously. At those points, a slowing dow

Year: 2001
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