  This paper examines the relaxation dynamics of a two-dimensional Coulomb
glass lattice model with high disorders. The study aims to investigate the
effects of disorder and Coulomb interactions on glassy dynamics by computing
the eigenvalue distribution of the linear dynamical matrix using mean-field
approximations. The findings highlight the significance of the single-particle
density of states (DOS) as the main controlling parameter affecting the
relaxation at intermediate and long times. For the model with unscreened
Coulomb interactions, our results indicate that the depletion of the DOS near
the Fermi level leads to logarithmic decay at intermediate times. As the
relaxation progresses to longer times, a power-law decay emerges, with the
exponent approaching zero as the disorder strength increases, suggesting the
manifestation of logarithmic decay at high disorders. The effects of screening
of interactions on the dynamics are also studied at various screening and
disorder strengths. The findings reveal that screening leads to the filling of
the gap in the density of states, causing deviation from logarithmic decay at
intermediate disorders. Moreover, in the strong disorder regime, the relaxation
dynamics are dominated by disorder, and even with screened Coulomb
interactions, the electronic relaxation remains similar to the unscreened case.
The time at which crossover to exponential decay occurs increases with
increasing disorder and interaction strength.
