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

We investigate a quantum Heisenberg model with both antiferromagnetic and disordered nearest-neighbor couplings. We use an extended dynamical mean-field approach, which reduces the lattice problem to a self-consistent local impurity problem that we solve by using a quantum Monte Carlo algorithm. We consider both two- and three-dimensional antiferromagnetic spin fluctuations and systematically analyze the effect of disorder. We find that in three dimensions for any small amount of disorder a spin-glass phase is realized. In two dimensions, while clean systems display the properties of a highly correlated spin-liquid (where the local spin susceptibility has a non-integer power-low frequency and/or temperature dependence), in the present case this behavior is more elusive unless disorder is very small. This is because the spin-glass transition temperature leaves only an intermediate temperature regime where the system can display the spin-liquid behavior, which turns out to be more apparent in the static than in the dynamical susceptibility.