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We investigate a quantum Heisenberg model with both antiferromagnetic anddisordered nearest-neighbor couplings. We use an extended dynamical mean-fieldapproach, which reduces the lattice problem to a self-consistent local impurityproblem that we solve by using a quantum Monte Carlo algorithm. We considerboth two- and three-dimensional antiferromagnetic spin fluctuations andsystematically analyze the effect of disorder. We find that in three dimensionsfor any small amount of disorder a spin-glass phase is realized. In twodimensions, while clean systems display the properties of a highly correlatedspin-liquid (where the local spin susceptibility has a non-integer power-lowfrequency and/or temperature dependence), in the present case this behavior ismore elusive unless disorder is very small. This is because the spin-glasstransition temperature leaves only an intermediate temperature regime where thesystem can display the spin-liquid behavior, which turns out to be moreapparent in the static than in the dynamical susceptibility.Comment: 15 pages, 7 figure

Disorder effects in the quantum Heisenberg model: Extended dynamical mean-field theory analysis