Charge and spin Drude weight of the one-dimensional extended Hubbard model at quarter-filling

TL;DR

This study uses advanced numerical methods to analyze charge and spin transport in the one-dimensional extended Hubbard model at quarter-filling, revealing phase-dependent behaviors and finite-size effects.

Contribution

It provides the first detailed numerical analysis of Drude weights in the extended Hubbard model across different interaction parameters using DMRG and compares results with theoretical predictions.

Findings

Charge Drude weight is discontinuous at the Kosterlitz-Thouless transition.

Spin Drude weight remains finite and varies smoothly across phases.

Finite-size scaling behaviors differ between metallic and insulating regions.

Abstract

We calculate the charge and spin Drude weight of the one-dimensional extended Hubbard model with on-site repulsion $U$ and nearest-neighbor repulsion $V$ at quarter filling using the density-matrix renormalization group method combined with a variational principle. Our numerical results for the Hubbard model (V=0) agree with exact results obtained from the Bethe ansatz solution. We obtain the contour map for both Drude weights in the $UV$-parameter space for repulsive interactions. We find that the charge Drude weight is discontinuous across the Kosterlitz-Thouless transition between the Luttinger liquid and the charge-density-wave insulator, while the spin Drude weight varies smoothly and remains finite in both phases. Our results can be generally understood using bosonization and renormalization group results. The finite-size scaling of the charge Drude weight is well fitted by a polynomial function of the inverse system size in the metallic region. In the insulating region we find an exponential decay of the finite-size corrections with the system size and a universal relation between the charge gap $\Delta_c$ and the correlation length $\xi$ which controls this exponential decay.