arXiv:cond-mat/9510114

Dimer Correlarions in Spin-1/2 Alternating XY Chain

Yôhei Saika, Kiyomi Okamoto

Published Oct 20, 1995• 0 citations

Abstract

We investigate the long-distance asymptotic behavior of the dimer correlations in the spin-1/2 alternating $XY$chain both at T=0 and at sufficiently low-temperatures. The correlations consist of the dimer long-range order part and the exponentially decaying one. Although the dimer long-range order takes the different values depending on the choice of the spin pairs, the behavior in the decaying term is same irrespective of the choice of spin pairs.

DOI: 10.48550/arxiv.cond-mat/9510114

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arXiv:cond-mat/9510114

Dimer Correlarions in Spin-1/2 Alternating XY Chain

Yôhei Saika, Kiyomi Okamoto

Published Oct 20, 1995• 0 citations

arXiv HTML PDF

Abstract

We investigate the long-distance asymptotic behavior of the dimer correlations in the spin-1/2 alternating

XY

chain both at T=0 and at sufficiently low-temperatures. The correlations consist of the dimer long-range order part and the exponentially decaying one. Although the dimer long-range order takes the different values depending on the choice of the spin pairs, the behavior in the decaying term is same irrespective of the choice of spin pairs.

DOI: 10.48550/arxiv.cond-mat/9510114

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We investigate the long-distance asymptotic behavior of the dimer correlations in the spin-1/2 alternating

XY

We exactly calculate the long-distance asymptotic behavior of the longitudinal spin correlation

R{\equiv}\langle S_{\imath}^{z}S_{\jmath}^{z}\rangle

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-time and long-distance asymptotic behavior of the

x

spin correlations at finite temperature in an anisotropic spin-1/2 XY chain is determined numerically. The decay of the correlations is exponential in both space and time. Similar exponential decay of correlations was already found earlier in the special case of the isotropic model, where analytical expressions for the decay rates could be derived via a mapping to a different model. While no such mapping is known for the anisotropic model, the asymptotic correlations can be very well approximated by a natural generalization of the known analytic results for the isotropic case.

The long-time and long-distance asymptotic behavior of the

x

{)}^{\mathit{r}}

c/${\mathit{r}}^{\mathrm{\ensuremath{\eta}}}$-

{\mathit{c}}_{1}

{\mathit{r}}^{2}

for large distance r. The power \ensuremath{\eta} depends on the Ising anisotropy, and \ensuremath{\eta}=0.405 at XY point and \ensuremath{\eta}=1.062 at Heisenberg point. For the two-dimensional square lattice, there is long-range staggered magnetization, and the dependence of magnetization on Ising anisotropy is given. For the crossover from one-dimensional linear chain to two-dimensional square lattice, we find that the disorder-order transition occurs as long as the interchain coupling is introduced. We believe that our method gives a unified approach to the long-range behavior of spin correlations in low-dimensional spin-1/2 antiferromagnets.