Localization of spin waves in disordered quantum rotors

We study the dynamics of excitations in a system of 0(N) quantum rotors in the presence of random fields and random anisotropies. Below the lower critical dimension d(1c) = 4 the system exhibits a quasi-long-range order with a power-law decay of correlations. At zero temperature the spin waves are localized at the length scale L-loc beyond which the quantum tunneling is exponentially suppressed, c similar to e(-(L/Lloc)2(theta+1)). At finite temperature T the spin waves propagate by thermal activation over energy barriers that scale as L-theta. Above d(1c) the system undergoes an order-disorder phase transition with activated dynamics such that the relaxation time grows with the correlation length xi as tau similar to e(C xi theta/T) at finite temperature and as tau similar to e(C'xi 2(theta+1)/h2) in the vicinity of the quantum critical point.