Symmetry-Protected Multifold Exceptional Points and Their Topological Characterization.

Area of Science:

• Non-Hermitian physics
• Topological phases of matter
• Quantum mechanics

Background:

• Exceptional points (EPs) are singularities in non-Hermitian systems, typically studied in 2D.
• Antiunitary symmetries, such as parity-time (PT) and charge-conjugation parity (CP), play a crucial role in system properties.
• Existing frameworks for topological phases are often limited to specific models.

Purpose of the Study:

• To investigate the stability and dimensionality of n-fold exceptional points (EPs) in non-Hermitian systems.
• To introduce a general theoretical framework for understanding symmetry-protected EPs beyond twofold.
• To apply this framework to a specific physical model and explore associated topological transitions.

Main Methods:

• Analysis of n-fold exceptional points (EPs) in non-Hermitian systems.
• Introduction of a resultant vector and its homotopy properties to quantify EP stability.
• Extension of the Z_{2} index concept for topological phases.
• Application to a frictional shallow water model.

Main Results:

• n-fold EPs are stable in n-1 dimensions under local antiunitary symmetries (PT, CP).
• Threefold and fourfold EPs are stable in 2D and 3D, respectively.
• A new framework based on homotopy properties of a resultant vector is established.
• The framework generalizes the Z_{2} index for PT/CP symmetric gapped phases.
• A frictional shallow water model exhibits threefold EPs with topological numbers ±1.
• Non-Hermitian topological transitions, including EP merging and recovery of forbidden propagation, are observed.

Conclusions:

• Symmetry-protected multifold exceptional points exhibit enhanced stability in higher dimensions.
• The developed theoretical framework provides a unified approach to understanding topological properties in non-Hermitian systems.
• The frictional shallow water model serves as a concrete example demonstrating the existence and implications of these phenomena.