Random Quantum Magnets with Long-Range Correlated Disorder: Enhancement of Critical and Griffiths-McCoy Singularities

We study the effect of spatial correlations in the quenched disorder on random quantum magnets at and near a quantum critical point. In the random transverse field Ising systems disorder correlations that decay algebraically with an exponent rho change the universality class of the transition for small enough rho and the off-critical Griffiths-McCoy singularities are enhanced. We present exact results for 1d utilizing a mapping to fractional Brownian motion and generalize the predictions for the critical exponents and the generalized dynamical exponent in the Griffiths phase to d>=2.