Tunneling of interacting one-dimensional electrons through a single scatterer: Luttinger liquid behavior in the Hartree-Fock model

TL;DR

This paper demonstrates that a self-consistent Hartree-Fock approach can reproduce key Luttinger liquid features, such as power-law tunneling and persistent current scaling, in one-dimensional electron systems with a delta barrier.

Contribution

It shows that the Hartree-Fock approximation captures universal Luttinger liquid behavior in 1D electron tunneling and persistent currents.

Findings

Transmission scales as L^{-2α} at the Fermi level.

Persistent current scales as L^{-1-α}.

Hartree-Fock reproduces Luttinger liquid features.

Abstract

We study tunneling of weakly-interacting spinless electrons at zero temperature through a single delta-barrier in one-dimensional wires and rings of finite lengths. Our numerical calculations are based on the self-consistent Hartree-Fock approximation, nevertheless, our results exhibit features known from correlated many-body models. In particular, the transmission in a wire of length L at the Fermi level is proportional to $L^{-2\alpha}$ with the universal power $\alpha$ (depending on the electron-electron interaction only, not on the strength of the delta-barrier). Similarly, the persistent current in a ring of the circumference $L$ obeys the rule $I\propto L^{-1-\alpha}$ known from the Luttinger liquid and Hubbard models. We show that the transmission at the Fermi level in the wire is related to the persistent current in the ring at the magnetic flux h/4e.