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We use a strong-disorder renormalization group (SDRG) method and ground-statequantum Monte Carlo (QMC) simulations to study S=1/2 spin chains with randomcouplings, calculating disorder-averaged spin and dimer correlations. The QMCsimulations demonstrate logarithmic corrections to the power-law decayingcorrelations obtained with the SDRG scheme. The same asymptotic forms applyboth for systems with standard Heisenberg exchange and for certain multi-spincouplings leading to spontaneous dimerization in the clean system. We show thatthe logarithmic corrections arise in the valence-bond (singlet pair) basis froma contribution that can not be generated by the SDRG scheme. In the model withmulti-spin couplings, where the clean system dimerizes spontaneously, randomsinglets form between spinons localized at domain walls in the presence ofdisorder. This amorphous valence-bond solid is asymptotically a random-singletstate and only differs from the random-exchange Heisenberg chain in itsshort-distance properties.

Properties of the random-singlet phase: from the disordered Heisenberg chain to an amorphous valence-bond solid