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arXiv:cond-mat/9905293 · Physical review. B, Condensed matter

Impurity spin relaxation in S=12XX chains

Joachim Stolze, Michael Vogel

Published Feb 1, 2000• 20 citations
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Abstract

Dynamic autocorrelations $〈{S}_{i}^{\ensuremath{\alpha}}{(t)S}_{i}^{\ensuremath{\alpha}}〉(\ensuremath{\alpha}=x,z)$ of an isolated impurity spin in a $S=\frac{1}{2}\mathrm{XX}$ 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; 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 fermion states.

DOI
10.1103/physrevb.61.4026

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In order to study the interplay between Kondo and Ruderman-Kittel-Kasuya-Yosida interaction, we calculate the spin-spin correlation functions between two Kondo impurities coupled to different sites of a half-filled open Hubbard chain. Using the density-matrix renormalization group (DMRG), we reexamine the exponents for the power-law decay of the correlation function between the two impurity spins as a function of the antiferromagnetic coupling JJJ, the Hubbard interaction UUU, and the distance RRR between the impurities. The exponents for finite systems obtained in this work deviate from previously published DMRG calculations. We furthermore show that the long-distance behavior of the exponents is the same for impurities coupled to the bulk or to both ends of the chain. We note that a universal exponent for the asymptotic behavior can not be extracted from these finite-size systems with open boundary conditions.
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The long-distance asymptotic behavior of the longitudinal spin correlation < S i z S j z > in the ground-state of the spin-1/2 dimerized XY chain is exactly calculated. The spin correlation < S i z S j z > decays in the exponential law with the correlation length ζ=1/ln [(1+δ)/(1-δ)]. Here δ (0≦δ≦1) represents the degree of alternation: i.e., the stronger and the weaker spin couplings are expressed as J (1+δ) and J (1-δ), respectively. The correlation length ξ smoothly changes from ∞ (power decay) to 0 as we move away from δ=0 (no alternation) to δ=1 (independent spin pairs). The nearest neighbor spin correlation is also investigated. The present results are compared with those obtained by the use of the phase Hamiltonian method.
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