NRG approach to the transport through a finite Hubbard chain connected to reservoirs

TL;DR

This paper investigates the low-energy transport properties of finite Hubbard chains connected to leads using NRG, revealing Fermi-liquid behavior and conductance characteristics related to chain length and interactions.

Contribution

It introduces a method to determine conductance from fixed-point energy levels in finite Hubbard chains, demonstrating Fermi-liquid behavior and transport differences based on chain length.

Findings

Even N_C shows exponential decrease in conductance with U, indicating a Mott-Hubbard gap.

Odd N_C maintains perfect transmission via Kondo resonance.

Low-energy states correspond to free quasi-particle excitations.

Abstract

We study the low-energy properties of a Hubbard chain of finite size N_C connected to two noninteracting leads using the numerical renormalization group (NRG) method. The results obtained for N_C = 3 and 4 show that the low-lying eigenstates have one-to-one correspondence with the free quasi-particle excitations of a local Fermi liquid. It enables us to determine the transport coefficients from the fixed-point Hamiltonian. At half-filling, the conductance for even N_C decreases exponentially with increasing U showing a tendency towards the development of a Mott-Hubbard gap. In contrast, for odd N_C, the Fermi-liquid nature of the low-energy states assures perfect transmission through the Kondo resonance. Our formulation to deduce the conductance from the fixed-point energy levels can be applied to various types of interacting systems.