Phase Coherence in a Random One-Dimensional System of Interacting Fermions: A Density Matrix Renormalization Group Study

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 $\DE= (-)^{N} (E(\phi=0) - E(\phi=\pi))$, where $\phi = 2\pi \Phi/\Phi_0$ ($N$ is the number of fermions, $\Phi$ the magnetic flux, and $\Phi_0=h/e$ the flux quantum), for a disordered system versus the system size $M$. The quantity $\ln{(M \DE)}$ is found to have a normal distribution to a good approximation. The ``localization length'' decreases (increases) for a repulsive (attractive) interaction.