Spin-spin correlations in the one-dimensional spin-1/2 antiferromagnetic Heisenberg chain

Hsueh‐Ju Lin, David K Campbell

Published Jan 1, 1990• 0 citations

Abstract

We have calculated the spin-spin correlations in the ground state of spin-1/2, one-dimensional, antiferromagnetic Heisenberg chain numerically. Using improved algorithms, we have been able to perform exact diagonalizations for lattices up to 30 sites and quantum Monte Carlo simulations for lattices up to 512 sites. This extensive range allows us to investigate the logarithmic dependence of spin-spin correlations. We present our results and discuss their implication. 11 refs., 1 fig., 2 tabs.

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Abstract

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{r}_{0}

${)}^{\ensuremath{\sigma}}$, with \ensuremath{\sigma}\ensuremath{\approxeq}0.2 to 0.3.

{\mathrm{Lo}}_{2}

{\mathrm{CuO}}_{4}

{)}^{\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.