Topological Field Theory of Non-Hermitian Systems

TL;DR

This paper develops a novel field-theoretical framework for understanding intrinsic non-Hermitian topological phases, revealing universal phenomena like unidirectional transport and skin effects, and predicting new effects induced by spatial textures.

Contribution

It introduces the first effective field theory for non-Hermitian topological phases, emphasizing spatial degrees of freedom and linking skin effects to anomalies.

Findings

Unified description of non-Hermitian topological phenomena

Prediction of new transport and skin effects in 2D systems

Identification of skin effect as an anomaly signature

Abstract

Non-Hermiticity gives rise to unique topological phases without Hermitian analogs. However, the effective field theory has yet to be established. Here, we develop a field-theoretical description of the intrinsic non-Hermitian topological phases. Because of the dissipative and nonequilibrium nature of non-Hermiticity, our theory is formulated solely in terms of spatial degrees of freedom, which contrasts with the conventional theory defined in spacetime. It provides the universal understanding about non-Hermitian topological phenomena, such as the unidirectional transport in one dimension and the chiral magnetic skin effect in three dimensions. Furthermore, it systematically predicts new physics; we illustrate this by revealing transport phenomena and skin effects in two dimensions induced by a perpendicular spatial texture. From the field-theoretical perspective, the non-Hermitian skin effect, which is anomalous localization due to non-Hermiticity, is shown to be a signature of an anomaly.