Exploring the impact of fluctuation-induced criticality on non-Hermitian skin effect and quantum sensors

In this paper we present a concrete example comparing the results predicted by non-Hermitian quantum mechanics with those of a more comprehensive description that considers environment-induced fluctuations. Our results highlight inaccuracies in the non-Hermitian model. Specifically, we investigate the non-Hermitian skin effect and sensor in the Hatano-Nelson model, contrasting it with a more precise Lindblad description. Our analysis reveals that these phenomena can undergo breakdown when environmental fluctuations come to the forefront, resulting in a nonequilibrium phase transition from a localized skin phase to a delocalized phase. Beyond this specific case study, we engage in a broader discussion regarding the interpretations and implications of non-Hermitian quantum mechanics. This examination serves to broaden our understanding of these phenomena and their potential consequences.