Real-space scaling methods applied to an interacting fermion Hamiltonian

Two different real-space techniques, the renormalization-group blocking method and finitecell scaling, are applied to a Hamiltonian of interacting fermions in one dimension which considers repulsion between electrons on neighboring sites. The localization transition which occurs at $T=0\mathrm{}$ when the strength of the electron repulsion increases is qualitatively well described by both techniques. However, the essential singularity which appears in the exact solution is only recovered by the finite-cell-scaling method.