Local density of states of the one-dimensional spinless fermion model

TL;DR

This study uses advanced numerical methods to analyze the local density of states in a one-dimensional spinless fermion model, confirming theoretical predictions and exploring boundary effects across the energy spectrum.

Contribution

It provides detailed DDMRG calculations of local density of states, validating Luttinger liquid theory exponents with high precision and analyzing boundary effects in the model.

Findings

Boundary effects influence local density of states at all energies.

Results agree with Luttinger liquid theory and Bethe Ansatz predictions.

Crossover from boundary to bulk density of states is characterized.

Abstract

We investigate the local density of states of the one-dimensional half-filled spinless fermion model with nearest-neighbor hopping t>0 and interaction V in its Luttinger liquid phase -2t < V <= 2t. The bulk density of states and the local density of states in open chains are calculated over the full band width 4t with an energy resolution <= 0.08t using the dynamical density-matrix renormalization group (DDMRG) method. We also perform DDMRG simulations with a resolution of 0.01t around the Fermi energy to reveal the power-law behaviour predicted by the Luttinger liquid theory for bulk and boundary density of states. The exponents are determined using a finite-size scaling analysis of DDMRG data for lattices with up to 3200 sites. The results agree with the exact exponents given by the Luttinger liquid theory combined with the Bethe Ansatz solution. The crossover from boundary to bulk density of states is analyzed. We have found that boundary effects can be seen in the local density of states at all energies even far away from the chain edges.