Imaginary gauge transformation in momentum space and Dirac exceptional point

TL;DR

This paper demonstrates that imaginary gauge transformations can be applied in momentum space, revealing equivalences between PT-symmetric non-Hermitian systems and Hermitian systems, and distinguishes two types of exceptional points, including a Dirac EP.

Contribution

It introduces the concept of imaginary gauge transformation in momentum space and identifies two types of exceptional points, including a Dirac EP, in gain-loss modulated systems.

Findings

Imaginary gauge transformation can be performed in momentum space.

Certain PT-symmetric systems are equivalent to Hermitian systems with real potentials.

Two types of exceptional points are distinguished, including a Dirac EP.

Abstract

An imaginary gauge transformation is at the core of the non-Hermitian skin effect. Here we show that such a transformation can be performed in momentum space as well, which reveals that certain gain and loss modulated systems in their parity-time (PT) symmetric phases are equivalent to Hermitian systems with real potentials. Our analysis in momentum space also distinguishes two types of exceptional points (EPs) in the same system. Besides the conventional type that leads to a PT transition upon the continuous increase of gain and loss, we find real-valued energy bands connected at a Dirac EP in hybrid dimensions, consisting of a spatial dimension and a synthetic dimension for the gain and loss strength.