Drude and Superfluid Weights in Extended Systems: the Role of Discontinuities and $\delta$-peaks in the One and Two-Body Momentum Densities

TL;DR

This paper investigates how discontinuities and delta peaks in momentum densities influence the Drude and superfluid weights, clarifying their roles in conductivity and localization in extended systems.

Contribution

It introduces a framework linking momentum density features to conductivity weights, highlighting the impact of delta peaks in two-body densities on both Drude and superfluid responses.

Findings

Discontinuities in momentum density contribute to the Drude weight.

Delta-function contributions in two-body densities affect both Drude and superfluid weights.

The connection between momentum density discontinuities and localization is established.

Abstract

The question of conductivity is revisited. Using the total momentum shift operator to construct the perturbed many-body Hamiltonian and ground state wave function the second derivative of the ground state energy with respect to the perturbing field is expressed in terms of the one and two-body momentum densities. The distinction between the adiabatic and envelope function derivatives, hence that between the Drude and superfluid weights can be introduced in a straightforward manner. It is shown that a discontinuity in the momentum density leads to a contribution to the Drude weight, but not the superfluid weight, however a $\delta$-function contribution in the two-body momentum density (such as in the BCS wave-funtion) contributes to both quantities. The connection between the discontinuity in the momentum density and localization is also demonstrated.