Discriminant indicators with generalized inversion symmetry

Abstract

We propose indicators of the discriminant for systems with generalized inversion symmetry which are computed from data only at high-symmetry points in the Brillouin zone. Our approach captures the exceptional points and their symmetry-protected variants without ambiguity arising from the reference energy, which is advantage over the previously known indicators for non-Hermitian systems. As demonstrations, we systematically analyze $3\times 3$-Hamiltonians where the proper choice of the reference energy is not obvious.

8 pages and 3 figures

References in corpus (9)

• The physics of exceptional points
• Topological Origin of Non-Hermitian Skin Effects
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Dynamically encircling exceptional points: Exact evolution and polarization state conversion
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Non-Hermitian Topological Theory of Finite-Lifetime Quasiparticles: Prediction of Bulk Fermi Arc Due to Exceptional Point
• Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian
• Non-Hermitian topology in rock-paper-scissors games

Cited by in corpus (7)

• Realizing exceptional points of any order in the presence of symmetry
• Protection of all nondefective twofold degeneracies by anti-unitary symmetries in non-Hermitian systems
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Winding Topology of Multifold Exceptional Points
• Discriminant indicator with generalized rotational symmetry
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Magnetic field effects on the Kitaev model coupled to environment