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We calculate the ground-state two-spin correlation functions of spin-1/2quantum Heisenberg chains with random exchange couplings using the real-spacerenormalization group scheme. We extend the conventional scheme to take accountof the contribution of local higher multiplet excitations in each decimationstep. This extended scheme can provide highly accurate numerical data for largesystems. The random average of staggered spin correlations of the chains withrandom antiferromagnetic (AF) couplings shows algebraic decay like $1/r^2$,which verifies the Fisher's analytic results. For chains with randomferromagnetic (FM) and AF couplings, the random average of generalizedstaggered correlations is found to decay more slowly than a power-law, in theform close to $1/\ln(r)$. The difference between the distribution functions ofthe spin correlations of the random AF chains and of the random FM-AF chains isalso discussed.Comment: 14 pages including 8 figures, REVTeX, submitted to Physical Review

Numerical renormalization-group study of spin correlations in one-dimensional random spin chains