Imaginary gauge transformation in momentum space and Dirac exceptional point

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.

arXiv comment8 pages, 9 figures

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Cited by in corpus (10)

• Enhanced Frequency Conversion in Parity-Time Symmetry Line
• Analysis of Dirac exceptional points and their isospectral Hermitian counterparts
• Extended imaginary gauge transformation in a general nonreciprocal lattice
• Non-Hermitian gauged laser arrays with localized excitations: Anomalous threshold and generalized principle of selective pumping
• Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
• Topological phase transition in fluctuating imaginary gauge fields
• Non-Hermitian systems with a real spectrum and selective skin effect
• Tunable Localisation in Parity-Time-Symmetric Resonator Arrays with Imaginary Gauge Potentials
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers