Protection of all nondefective twofold degeneracies by anti-unitary symmetries in non-Hermitian systems

Abstract

Non-Hermitian degeneracies are classified as defective and nondefective exceptional points~(EP). While in defective EPs, both eigenvalues and eigenenergies coalesce, nondefective EPs are characterized merely by the occurrence of degeneracies in their eigenvalues. It is also known that all degeneracies are either symmetry-protected or accidental. In this paper, I prove that anti-unitary symmetries protect all nondefective twofold EPs. By developing a 2D non-Hermitian tight-binding model, I have demonstrated that these symmetries are composite of various symmetry operations such as discrete or spatial point-group symmetries and Wick's rotation in the non-Hermitian parameter space. Introducing these composite symmetries, I present the protection of nondefective EPs in various parameter regimes of my model. This work paves the way to stabilizing nondefective EPs and offers a new perspective on understanding non-Hermitian band crossings.

arXiv comment4+6 pages, 2+9 figures

References in corpus (68)

• Weyl and Dirac Semimetals in Three Dimensional Solids
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Symmetry and Topology in Non-Hermitian Physics
• Topological Origin of Non-Hermitian Skin Effects
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• Topological Band Theory for Non-Hermitian Hamiltonians
• Loss-induced suppression and revival of lasing
• Topolectrical circuit realization of topological corner modes
• Non-Hermitian Boundary Modes
• Quantized circular photogalvanic effect in Weyl semimetals
• Multiple types of topological fermions in transition metal silicides
• Reciprocal skin effect and its realization in a topolectrical circuit
• A new type of Weyl semimetal with quadratic double Weyl fermions in SrSi2
• Creating stable Floquet-Weyl semimetals by laser-driving of 3D Dirac materials
• Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Symmetry and Higher-Order Exceptional Points
• Topological semimetal in a fermionic optical lattice
• Accidental degeneracy and topological phase transitions in two-dimensional core-shell dielectric photonic crystals
• Symmetry-protected multifold exceptional points and their topological characterization
• Review of experiments on the chiral anomaly in Dirac-Weyl semimetals
• Fermion doubling theorems in 2D non-Hermitian systems for Fermi points and exceptional points
• Three-component fermions with surface Fermi arcs in topological semimetal tungsten carbide
• Non-Hermitian Dirac Cones
• Non-Hermitian chiral phononics through optomechanically-induced squeezing
• Probing topology by "heating": Quantized circular dichroism in ultracold atoms
• Exceptional rings protected by emergent symmetry for mechanical systems
• Experimental Realization of Weyl Exceptional Rings in a Synthetic Three-Dimensional Non-Hermitian Phononic Crystal
• Guided accumulation of active particles by topological design of a second-order skin effect
• Active topolectrical circuits
• Topological Field Theory of Non-Hermitian Systems
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• Electric circuits for non-Hermitian Chern insulators
• Realizing exceptional points of any order in the presence of symmetry
• Observation of quadratic Weyl points and double-helicoid arcs
• Multifold nodal points in magnetic materials
• Hidden-Symmetry-Protected Topological Semimetals on a Square Lattice
• Quantized classical response from spectral winding topology
• Exceptional non-Hermitian topological edge mode and its application to active matter
• Non-Hermitian physics without gain or loss: the skin effect of reflected waves
• Symmetry protected topological phases characterized by isolated exceptional points
• $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian Dirac semimetals
• Observation of multiple types of topological fermions in PdBiSe
• Non-Hermitian bidirectional robust transport
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Entanglement Spectrum Crossings Reveal non-Hermitian Dynamical Topology
• Non-Hermitian topology in monitored quantum circuits
• Thermal and gravitational chiral anomaly induced magneto-transport in Weyl semimetals
• Compatibility of transport effects in non-Hermitian nonreciprocal systems
• Coexistence of orbital degeneracy lifting and superconductivity in iron-based superconductors
• Chiral anomaly induced nonlinear Nernst and thermal Hall effects in Weyl semimetals
• Exceptional points in the one-dimensional Hubbard model
• Relaxation to a Parity-Time Symmetric Generalized Gibbs Ensemble after a Quantum Quench in a Driven-Dissipative Kitaev Chain
• Controllable unidirectional transport and photon storage in an one-dimensional lattice with complex hopping rates
• Degeneracy and defectiveness in non-Hermitian systems with open boundary
• Chiral symmetry in non-Hermitian systems: product rule and Clifford algebra
• Hidden antiunitary symmetry behind "accidental" degeneracy and its protection of degeneracy
• Non-Hermitian chiral anomalies
• Consistent description of field theories with non-Hermitian mass terms
• Quantized electrochemical transport in Weyl semimetals
• Accidental Degeneracy in k-space, Geometrical Phase, and the Perturbation of $\pi$ by Spin-orbit Interactions
• Discriminant indicators with generalized inversion symmetry
• Simulating non-Hermitian dynamics of a multi-spin quantum system and an emergent central spin model
• Hidden-symmetry-protected Z_2 topological insulator in a cubic lattice
• Self-healing of non-Hermitian topological skin modes

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• Non-Hermitian chiral anomalies in interacting systems