Using the density-matrix renormalization-group algorithm, we study the model of spinless fermions with nearest-neighbor interaction on a ring in the presence of disorder. We determine the spatial decay of the density induced by a defect (Friedel oscillations), and the phase sensitivity of the ground-state energy ΔE=(-${)}^{\mathit{N}}$[E(φ=0)-E(φ=π)], where φ=2πΦ/${\mathrm{\Phi }}_0$ (N is the number of fermions, Φ the magnetic flux, and ${\mathrm{\Phi }}_0$=h/e the flux quantum), for a disordered system versus the system size M. The quantity ln(MΔE) is found to have a normal distribution to a good approximation. The ‘‘localization length’’ decreases (increases) for a repulsive (attractive) interaction. © 1996 The American Physical Society.

• Received 27 February 1996

DOI:https://doi.org/10.1103/PhysRevB.53.15397