Explore the perturbative calculation of the out-of-time-ordered correlator (OTOC) in the deep many-body localized regime of the disordered Heisenberg XXZ model in this 33-minute conference talk. Discover how the OTOC measured in the Fock space indicates lower and upper bounds of information propagation speed, constructing a highly structured light cone confined in strictly logarithmic bounds. Examine the analytic expression of OTOC associated with the slowest scrambling along the upper logarithmic light cone. Learn about an effective Hamiltonian with a reduced Hilbert space for the lowest order perturbation calculation of OTOC related to the lower light cone of the fastest scrambling. Investigate the application of this method to both 1D and 2D lattices, providing evidence that logarithmic bounds of information scrambling may be valid in higher dimensions under strong disorder and weak hopping conditions.