Persistent current and Drude weight for the one-dimensional Hubbard model from current lattice density functional theory

TL;DR

This paper extends lattice density functional theory to include current effects, enabling accurate and efficient calculations of persistent currents and Drude weights in one-dimensional Hubbard rings with and without impurities.

Contribution

The authors develop a current-dependent lattice density functional theory for the Hubbard model, improving the calculation of transport properties in one-dimensional correlated systems.

Findings

LDA-CLDFT accurately predicts ground state energies in the metallic phase.

Persistent currents depend on Coulomb and impurity interactions as captured by LDA-CLDFT.

The method effectively models the influence of ring size on transport properties.

Abstract

The Bethe-Ansatz local density approximation (LDA) to lattice density functional theory (LDFT) for the one-dimensional repulsive Hubbard model is extended to current-LDFT (CLDFT). The transport properties of mesoscopic Hubbard rings threaded by a magnetic flux are then systematically investigated by this scheme. In particular we present calculations of ground state energies, persistent currents and Drude weights for both a repulsive homogeneous and a single impurity Hubbard model. Our results for the ground state energies in the metallic phase compares favorably well with those obtained with numerically accurate many-body techniques. Also the dependence of the persistent currents on the Coulomb and the impurity interaction strength, and on the ring size are all well captured by LDA-CLDFT. Our study demonstrates that CLDFT is a powerful tool for studying one-dimensional correlated electron systems with high accuracy and low computational costs.