NRG Study of an Inversion-Symmetric Interacting Model: Universal Aspects of its Quantum Conductance

TL;DR

This study uses the numerical renormalization group to analyze an inversion-symmetric interacting model, revealing universal behaviors in quantum conductance related to key parameters and fixed points, especially in the non-perturbative regime.

Contribution

It maps a spinless fermion scattering model onto an Anderson model and identifies universal conductance functions depending on parameter ratios.

Findings

Identifies a line of free-fermion fixed points at zero temperature.

Derives universal functions for quantum conductance based on parameter ratios.

Shows the universal regime becomes non-perturbative when interaction U exceeds level width .

Abstract

We consider scattering of spinless fermions by an inversion-symmetric interacting model characterized by three parameters (interaction U, internal hopping t_d and coupling t_c). Mapping this spinless model onto an Anderson model with Zeeman field, we use thenumerical renormalization group for studying the particle-hole symmetric case. We show that the zero temperature limit is characterized by a line of free-fermion fixed points and a scale \tau(U,t_c) of t_d for which there is perfect transmission. The quantum conductance and the low energy excitations of the model are given by universal functions of t_d/\tau if t_d < \Gamma and of t_d/t_c^2 if t_d > \Gamma, \Gamma = t_c^2 being the level width of the scatterer. This universal regime becomes non-perturbative when U exceeds \Gamma.