2021/06/30 by Karol Kawa, Paweł Machnikowski
Physics and Astronomy · #Quantum and electron transport phenomena #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.dis-nn #quant-ph
paper · pdf · doi:10.1103/physrevb.105.184204
published as Phys. Rev. B 105, 184204 (2022)
openalex created_date 2021/06/22 · arxiv created 2021/07/01 · openalex publication_date 2022/05/18 · openalex updated_date 2026/07/28 · arxiv updated 2026/08/04
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 (\ensuremath∝r^\ensuremath-\ensuremathμ). 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 \ensuremathμ=1, the propagation starts as a ballistic motion and then, at a certain crossover time, turns into standard diffusion.