Disorder effects in the quantum Heisenberg model: 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 noninteger power-law frequency and temperature dependence), in the present case this behavior is more elusive unless disorder is very small. In fact the spin-glass transition temperature leaves only a limited intermediate temperature regime, where the system displays the spin-liquid behavior.