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

TL;DR

This study uses the density matrix renormalization group to analyze phase coherence and localization in disordered one-dimensional interacting fermion systems, revealing how interactions influence localization length and phase sensitivity.

Contribution

It provides a detailed numerical analysis of phase coherence and localization in disordered 1D fermion systems with interactions, highlighting the effects of repulsive and attractive forces.

Findings

Localization length decreases with repulsive interaction.

Localization length increases with attractive interaction.

The distribution of ln(MΔE) is approximately normal.

Abstract

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.