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

We study the effect of spatial correlations on quenched disorder in random quantum magnets at and near a quantum critical point. In 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 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 $d\ge 2$.