Non-equilibrium transport through a model quantum dot: Hartree-Fock approximation and beyond

TL;DR

This paper investigates the finite-temperature transport in a spinless fermion quantum dot model using Hartree-Fock approximation, comparing results with analytical and numerical data to assess its accuracy and limitations.

Contribution

It applies the time-dependent Hartree-Fock method to model quantum dot transport and evaluates its effectiveness against known analytical and numerical results.

Findings

HF reproduces main features of I-V characteristics in weak interactions

HF fails to capture subtle power-law behaviors in the model

Comparison highlights limitations of HF in strongly correlated regimes

Abstract

The finite-temperature transport properties of the spinless interacting fermion model coupled to non-interacting leads are investigated. Employing the unrestricted time-dependent Hartree-Fock (HF) approximation, the transmission probability and the non-linear $I$-$V$ characteristics are calculated, and compared with available analytical results and with numerical data obtained from a Hubbard-Stratonovich decoupling of the interaction. In the weak interaction regime, the HF approximation reproduces the gross features of the exact $I$-$V$ characteristics but fails to account for subtle properties like the particular power law for the reflected current in the interacting resonant level model.