Abstract
Friedel oscillations are ubiquitous around localized defects in Hermitian quantum mechanics. Here we study their fate around a non-Hermitian, imaginary impurity and evaluate the corresponding non-Hermitian Lindhard function in one dimension, where quantum effects are traditionally enhanced due to spatial confinement. Most importantly, we find that the static limit of the non-Hermitian Lindhard function has no divergence at twice the Fermi wave number and vanishes identically for all other wave numbers 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 a heavily suppressed density response, respectively.
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