Symmetry and Higher-Order Exceptional Points

Area of Science:

• Quantum mechanics
• Non-Hermitian physics
• Condensed matter theory

Background:

• Exceptional points (EPs) are unique degeneracies in non-Hermitian systems where eigenvalues and eigenvectors coalesce.
• Second-order EPs are well-studied due to their relative ease of creation, requiring two real parameters.
• Higher-order EPs are generally considered rare and require significant fine-tuning.

Purpose of the Study:

• To investigate the role of symmetries in the abundance and properties of higher-order exceptional points.
• To demonstrate that symmetries can make higher-order EPs more accessible and conceptually rich.
• To explore the distinct topological features and protection mechanisms of different symmetry-protected EPs.

Main Methods:

• Theoretical analysis of non-Hermitian systems with specific symmetries.
• Investigation of third-order exceptional points under parity-time (PT) and generalized chiral symmetries.
• Modeling of EPs in simple physical systems, including non-Hermitian Lieb lattice models.

Main Results:

• Physically relevant symmetries significantly enhance the abundance and richness of higher-order EPs.
• Third-order EPs generically require only two real tuning parameters when protected by PT or chiral symmetry.
• Different symmetries lead to topologically distinct EPs: PT symmetry protects ∼k^{1/3} dispersion, while chiral symmetry protects ∼k^{1/2} dispersion.

Conclusions:

• Symmetries are crucial for understanding the prevalence and behavior of higher-order exceptional points.
• Symmetry protection leads to distinct topological properties and dispersion relations for higher-order EPs.
• The study identifies stable, weak, and fragile aspects of symmetry-protected higher-order EPs and their associated phenomena.