Universal scaling of Green's functions in disordered non-Hermitian systems

TL;DR

This paper uncovers universal scaling laws for Green's functions in disordered non-Hermitian systems, revealing distinct phases and providing analytical and experimental insights into their response behaviors.

Contribution

It introduces a universal scaling framework for Green's functions in disordered non-Hermitian systems, combining numerical, analytical, and experimental perspectives.

Findings

Identification of exponential and algebraic growth phases in Green's functions.

Analytical explanation of scaling behaviors using large deviation theory.

Experimental relevance in steady states of disordered open quantum systems.

Abstract

The competition between non-Hermitian skin effect and Anderson localization leads to various intriguing phenomena concerning spectrums and wavefunctions. Here, we study the linear response of disordered non-Hermitian systems, which is precisely described by the Green's function. We show that the average maximum value of matrix elements of Green's functions, which quantifies the maximal response against an external perturbation, exhibits different phases characterized by different scaling behaviors with respect to the system size. Whereas the exponential-growth phase is also seen in the translation-invariant systems, the algebraic-growth phase is unique to disordered non-Hermitian systems. We explain the numerical findings using the large deviation theory, which provides analytical insights into the algebraic scaling factors of non-Hermitian disordered Green's functions. Furthermore, we show that these scaling behaviors can be observed in the steady states of disordered open quantum systems, offering a quantum-mechanical avenue for their experimental detection. Our work highlights an unexpected interplay between non-Hermitian skin effect and Anderson localization.