Extended quasiparticle Pad\'e approximation for non-Fermi liquids

TL;DR

This paper introduces an extended quasiparticle Padé approximation for non-Fermi liquids, effectively capturing spectral functions and transport properties, and revealing impurity-induced phenomena like localization and potential superconductivity.

Contribution

It develops a novel Padé approximation method that interpolates between known limits for non-Fermi liquids and demonstrates its effectiveness across various models.

Findings

The approximation fulfills sum rules regardless of the interpolating function.

Spectral functions and momentum distributions are accurately reproduced without a Fermi surface jump.

Impurity effects lead to localization and a maximum in conductivity suggestive of impurity-triggered superconductivity.

Abstract

The extended quasiparticle picture is adapted to non-Fermi systems by suggesting a Pad\'e approximation which interpolates between the known small scattering-rate expansion and the deviation from the Fermi energy. The first two energy-weighted sum rules are shown to be fulfilled independent of the interpolating function for any selfenergy. For various models of one-dimensional Fermions scattering with impurities the quality of the Pad\'e approximation for the spectral function is demonstrated and the reduced density matrix or momentum distribution is reproduced not possessing a jump at the Fermi energy. Though the two-fold expansion is necessary to realize the spectral function and reduced density, the extended quasiparticle approximation itself is sufficient for the description of transport properties due to cancellation of divergent terms under integration. The T-matrix approximation leads to the delay time as the time two particles spend in a correlated state. This contributes to the reduced density matrix and to an additional part in the conductivity which is presented at zero and finite temperatures. Besides a localization at certain impurity concentrations, the conductivity shows a maximum at small temperatures interpreted as onset of superconducting behaviour triggered by impurities. The Tan contact reveals the same universal behaviour as known from electron-electron scattering.