Can banded random matrices describe realistic many-body quantum systems?*

Despite the success of full random matrices in describing statistically the spectrum of complex systems, they imply the unphysical scenario of all particles interacting simultaneously. Banded random matrices were introduced in an effort to better approach random matrices to realistic systems. We study power-law banded random matrices and show that they capture very well many features of the evolution of realistic disordered spin-1/2 chains both in their chaotic regime and in intermediate regions between chaos and localization.