Multispeed Prethermalization in Quantum Spin Models with Power-Law Decaying Interactions.

The relaxation of uniform quantum systems with finite-range interactions after a quench is generically driven by the ballistic propagation of long-lived quasiparticle excitations triggered by a sufficiently small quench. Here we investigate the case of long-range (1/r^{α}) interactions for a d-dimensional lattice spin model with uniaxial symmetry, and show that, in the regime d<α<d+2, the entanglement and correlation buildup is radically altered by the existence of a nonlinear dispersion relation of quasiparticles, ω∼k^{z<1}, at small wave vectors, leading to a divergence of the quasiparticle group velocity and superballistic propagation. This translates in a superlinear growth of correlation fronts with time and sublinear growth of relaxation times of subsystem observables with size when focusing on k=0 fluctuations. Yet the large dispersion in group velocities leads to an extreme wavelength dependence of relaxation times of finite-k fluctuations, with entanglement being susceptible to all of them. Our predictions are directly relevant to current experiments probing the nonequilibrium dynamics of trapped ions, or ultracold magnetic and Rydberg atoms in optical lattices.