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We study XY and dimerized XX spin-1/2 chains with random exchange couplingsby analytical and numerical methods and scaling considerations. We extendprevious investigations to dynamical properties, to surface quantities andoperator profiles, and give a detailed analysis of the Griffiths phase. Wepresent a phenomenological scaling theory of average quantities based on thescaling properties of rare regions, in which the distribution of the couplingsfollows a surviving random walk character. Using this theory we have obtainedthe complete set of critical decay exponents of the random XY and XX models,both in the volume and at the surface. The scaling results are confronted withnumerical calculations based on a mapping to free fermions, which then lead toan exact correspondence with directed walks. The numerically calculatedcritical operator profiles on large finite systems (L<=512) are found to followconformal predictions with the decay exponents of the phenomenological scalingtheory. Dynamical correlations in the critical state are in averagelogarithmically slow and their distribution show multi-scaling character. Inthe Griffiths phase, which is an extended part of the off-critical regionaverage autocorrelations have a power-law form with a non-universal decayexponent, which is analytically calculated. We note on extensions of our workto the random antiferromagnetic XXZ chain and to higher dimensions.Comment: 19 pages RevTeX, eps-figures include

Random antiferromagnetic quantum spin chains: Exact results from scaling of rare regions