We exactly calculate the long-distance asymptotic behavior of the longitudinal spin correlation R≡⟨SzSz⟩ of the spin-1/2 dimerized XY chain at finite temperatures. The spin correlation R decays in the exponential law with the correlation length ξ( T ), which decreases with the increase of T . The present results are compared with those obtained by the use of the phase Hamiltonian method.
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.