Spread of correlations in strongly disordered lattice systems with long-range coupling

We investigate the spread of correlations in a one-dimensional lattice system with high on-site energy disorder and long-range couplings with a power-law dependence on the distance (proportional to r(-mu)). The increase in correlation between the initially quenched node and a given node exhibits three phases: quadratic in time, linear in time, and saturation. No further evolution is observed in the long time regime. We find an approximate solution of the model valid in the limit of strong disorder and reproduce the results of numerical simulations with analytical formulas. We also find the time needed to reach a given correlation value as a measure of the propagation speed. Because of the triple-phase evolution of the correlation function, the propagation changes its time dependence. In the particular case of mu = 1, the propagation starts as a ballistic motion and then, at a certain crossover time, turns into standard diffusion.

Automated summary

In this study, we investigate the spread of correlations in a one-dimensional lattice system with high on-site energy disorder and long-range couplings. We find that the increase in correlation between two nodes exhibits three phases and we also obtain an approximate solution of the model valid in the limit of strong disorder.