Non-Hermitian Delocalization Induced by Residue Imaginary Velocity

TL;DR

This paper uncovers a novel delocalization mechanism in non-Hermitian quantum systems driven by residue imaginary velocity, affecting collective properties even when single-particle states are localized, with implications for experiments and applications.

Contribution

It introduces the concept of residue imaginary velocity as a new delocalization mechanism in non-Hermitian systems, expanding understanding beyond traditional wavefunction-based localization.

Findings

Delocalization occurs in collective properties despite localized eigenstates.

Residue imaginary velocity can induce delocalization at finite temperatures and with interactions.

Disorder affecting imaginary velocity can also lead to strong-disorder delocalization.

Abstract

The dichotomy of localization versus delocalization is a historic topic central to quantum and condensed matter physics. We discover a new delocalization mechanism attributed to a residue imaginary (part of) velocity $\operatorname{Im}(v)$, feasible for ground states or low-temperature states of non-Hermitian quantum systems under periodic boundary conditions. In sharp contrast to conventional formalisms through extended wavefunctions, these target systems exhibit delocalization in collective physical properties such as correlation and entanglement (of the Fermi Seas) despite sometimes localized left and right single-particle eigenstates, as we demonstrate numerically and generalize to scenarios with finite temperatures and interaction. Interestingly, disorder contributing to $\operatorname{Im}(v)$ may also allow strong-disorder delocalization. Thus, the nontrivial physics of $\operatorname{Im}(v)$ significantly enriches our understanding of delocalization and harbors interesting experiments and practical applications.