Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory

TL;DR

This paper explores how strong electron correlations influence the non-Hermitian skin effect in a Hubbard model with asymmetric hopping, revealing a tunable interplay that affects boundary localization and transport properties.

Contribution

It introduces real-space dynamical mean-field theory to study the combined effects of non-Hermiticity and correlations in the Hubbard model, a novel approach in this context.

Findings

Correlations can suppress the skin effect at moderate asymmetric hopping.

Strong asymmetric hopping can restore amplification even with strong interactions.

The study reveals a crossover from boundary-dominated to correlation-driven dynamics.

Abstract

Non-Hermitian quantum systems, characterized by their ability to model open systems with gain and loss, have unveiled striking phenomena such as the non-Hermitian skin effect (NHSE), where eigenstates localize at boundaries under open boundary conditions. While extensively studied in non-interacting systems, the interplay between NHSE and strong electron correlations remains largely unexplored. Here, we investigate the non-Hermitian Hubbard model with asymmetric hopping, employing real-space dynamical mean-field theory (R-DMFT), a novel extension to such non-Hermitian correlated models-to capture both local correlations and spatial inhomogeneities. By analyzing the end-to-end Green's function as probes of directional amplification, we demonstrate that strong correlations can suppress the skin effect, leading to a crossover from boundary-dominated to correlation-driven dynamics. Our systematic study reveals that correlations dominate at small to intermediate strength of asymmetric hopping, inducing exponential decay in the end-to-end Green's function, but higher strength of asymmetric hopping can restore amplification even at strong interaction. These results illuminate the tunable interplay between correlations and non-Hermitian physics, suggesting avenues for engineering non-reciprocal transport in correlated open quantum systems.