Non-Hermitian Lindhard function and Friedel oscillations

TL;DR

This paper investigates the non-Hermitian Lindhard function in one dimension, revealing that it does not produce Friedel oscillations at zero temperature, contrasting with the Hermitian case, through analytical and numerical methods.

Contribution

It introduces the non-Hermitian Lindhard function, analyzes its behavior, and demonstrates the absence of Friedel oscillations at zero temperature, a novel insight in many-body physics.

Findings

Non-Hermitian Lindhard function lacks divergence at twice the Fermi wavenumber.

No Friedel oscillations are induced by imaginary impurities at zero temperature.

Numerical simulations confirm the analytical results with weak real or imaginary potentials.

Abstract

The Lindhard function represents the basic building block of many-body physics and accounts for charge response, plasmons, screening, Friedel oscillation, RKKY interaction etc. Here we study its non-Hermitian version in one dimension, where quantum effects are traditionally enhanced due to spatial confinement, and analyze its behavior in various limits of interest. Most importantly, we find that the static limit of the non-Hermitian Lindhard function has no divergence at twice the Fermi wavenumber and vanishes identically for all other wavenumbers at zero temperature. Consequently, no Friedel oscillations are induced by a non-Hermitian, imaginary impurity to lowest order in the impurity potential at zero temperature. Our findings are corroborated numerically on a tight-binding ring by switching on a weak real or imaginary potential. We identify conventional Friedel oscillations or heavily suppressed density response, respectively.