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arXiv:1604.00939 · Physical review. B./Physical review. B

Exact asymptotic correlation functions of bilinear spin operators of the Heisenberg antiferromagnetic spin- 12 chain

T. Vekua, Gaoyong Sun

Published Jul 14, 2016• 7 citations
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Abstract

Exact asymptotic expressions of the uniform parts of the two-point correlation functions of bilinear spin operators in the Heisenberg antiferromagnetic spin-$\frac{1}{2}$ chain are obtained. Apart from the algebraic decay, the logarithmic contribution is identified, and the numerical prefactor is determined. We also confirm numerically the multiplicative logarithmic correction of the staggered part of the bilinear spin operators $\ensuremath{\langle}\ensuremath{\langle}{S}_{0}^{a}{S}_{1}^{a}{S}_{r}^{b}{S}_{r+1}^{b}\ensuremath{\rangle}\ensuremath{\rangle}={(\ensuremath{-}1)}^{r}d/(r{ln}^{\frac{3}{2}}r)+(3{\ensuremath{\delta}}_{a,b}\ensuremath{-}1){ln}^{2}r/(12{\ensuremath{\pi}}^{4}{r}^{4})$, and estimate the numerical prefactor as $d\ensuremath{\simeq}0.067$. The relevance of our results for ground-state fidelity susceptibility at the Berezinskii-Kosterlitz-Thouless quantum phase transition points in one-dimensional systems is discussed at the end of our work.

DOI
10.1103/physrevb.94.014417

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We calculate the ground-state two-spin correlation functions of spin-12\frac{1}{2}21​ quantum Heisenberg chains with random exchange couplings using the real-space renormalization-group scheme. We extend the conventional scheme to take account of the contribution of local higher multiplet excitations in each decimation step. This extended scheme can provide highly accurate numerical data for large systems. The random average of staggered spin correlations of the chains with random antiferromagnetic (AF) couplings shows algebraic decay like 1/r2,{1/r}^{2},1/r2, which verifies the Fisher's analytic results. For chains with random ferromagnetic (FM) and AF couplings, the random average of generalized staggered correlations is found to decay more slowly than a power law, in the form close to 1/ln(r).1/\mathrm{ln}(r).1/ln(r). The difference between the distribution functions of the spin correlations of the random AF chains and of the random FM-AF chains is also discussed.
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