Renormalization-group approach to quantum percolation and Anderson localization.

Abstract

We study the quantum site percolation problem, which is defined by a substitutionally disordered tight-binding Hamiltonian, with a large-cell or macroscopic renormalization-group approach. Our estimate for the quantum percolation threshold ${p}_{q}$ is 0.45 for a simple-cubic lattice, which should be compared with the classical percolation threshold of ${p}_{c}$=0.3117. To test the reliability of our method we have also calculated ${p}_{c}$ and have evaluated (W/J${)}_{c}$ for the usual Anderson model. In both cases our results are in reasonable agreement with previous studies.