Analytical calculation of the Green's function and Drude weight for a correlated fermion-boson system

TL;DR

This paper analytically calculates the Green's function and Drude weight for a correlated fermion-boson system, revealing transport properties beyond classical Drude theory due to strong correlations.

Contribution

It introduces an analytical method to compute Green's function and Drude weight in a fermion-boson system with strong correlations, extending understanding of quantum transport.

Findings

Green's function and Drude weight are calculated analytically.

Transport cannot be described by classical Drude parameters.

The Drude weight provides insight into correlated quantum transport.

Abstract

In classical Drude theory the conductivity is determined by the mass of the propagating particles and the mean free path between two scattering events. For a quantum particle this simple picture of diffusive transport loses relevance if strong correlations dominate the particle motion. We study a situation where the propagation of a fermionic particle is possible only through creation and annihilation of local bosonic excitations. This correlated quantum transport process is outside the Drude picture, since one cannot distinguish between free propagation and intermittent scattering. The characterization of transport is possible using the Drude weight obtained from the f-sum rule, although its interpretation in terms of free mass and mean free path breaks down. For the situation studied we calculate the Green's function and Drude weight using a Green's functions expansion technique, and discuss their physical meaning.