A Renormalization-Group Study Of The Anderson Hamiltonian For Arbitrary Band-Filling

The Anderson hamiltonian has been studied for arbitrarily filled bands using the real space renormalization group (RSRG) method. The ground state energy is determined in one dimension for the scale factors ns = 3 and ns = 5. Direct application of RSRG gives, for a certain ns, the results for only ns number of discrete cases of band-filling. We then devise an interpolation scheme which spans the entire region of the band and gives the ground state energy for any general filling. The results, as provided by our scheme, satisfy the desired particle-hole symmetry exactly and are always an upper bound to the exact one. The non-linear dependence of the band energy on its filling is represented correctly, even for small ns. Finally, we discuss how the results improve for large ns.