Characterizing the many-body localization (MBL) transition in strongly disordered and interacting quantum systems is an important issue in the field of condensed matter physics. We study the single particle Greens functions for a disordered interacting system in one dimension using exact diagnonalization in the infinite temperature limit. We provide strong evidence that the typical values of the local density of states and the scattering rate, evaluated using the computed eigenstate Greens functions and self energies, can be used to track the delocalization to MBL transition. In the delocalized phase, the typical values of the local density of states and the scattering rate are of the order of the corresponding average values while in the MBL phase, the typical values for both the quantities become vanishingly small. The probability distribution functions of the local density of states and the scattering rate are broad log-normal distributions in the delocalized phase while the distributions become very narrow and sharply peaked close to zero in the MBL phase. We also study the eigenstate Greens function for all the many-body eigenstates and demonstrate that both, the energy resolved typical scattering rate and the typical local density of states, carry signatures of the many-body mobility edges.
تحميل البحث