Non-Hermitian Delocalization Induced by Residue Imaginary Velocity

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.