Diffusion of excitations and power-law localization in strongly disordered systems with long-range coupling

Abstract

We investigate the spread of correlations carried by an excitation in a 1-dimensional lattice system with high on-site energy disorder and long-range couplings with a power-law dependence on the distance (∝ r −µ ). 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 µ = 1, the propagation starts as a ballistic motion, then, at a certain crossover time, turns into standard diffusion.

Sub-diffusive phases in open clean long-range systems

“…Interestingly, one-dimensional long-range lattice systems have received significant attention in recent times due to the possibility of realizing such interactions in an experimentally controlled fashion in several platforms such as Rydberg atoms [28][29][30][31], trapped ions [32][33][34][35][36][37][38][39][40], polar molecules [41][42][43] , dipolar gas [44], nuclear spins [45], nitrogen-vacancy centers in diamond and trapped atoms [46], and demonstrating exotic physics, e.g., time crystals [39,46], prethermalization [34], dynamical phase transitions [33,38,45,47], environment assisted transport [40] etc. This has lead to interesting set of studies for quantum transport which so far has been limited to isolated systems in presence and absence of disorder [27,[48][49][50][51][52][53][54][55], and one spin chain with Lindblad boundary-driving [56]. To our knowledge, transport through one-dimensional long-range systems has not been studied before in a non-Markovian open quantum system setting, as we do here using non-equilibrium-Greens-function (NEGF) and reveal the remarkable sub-diffusive phases with no isolated system analogue.…”