Realizing exceptional points of any order in the presence of symmetry

Abstract

Exceptional points~(EPs) appear as degeneracies in the spectrum of non-Hermitian matrices at which the eigenvectors coalesce. In general, an EP of order $n$ may find room to emerge if $2(n-1)$ real constraints are imposed. Our results show that these constraints can be expressed in terms of the determinant and traces of the non-Hermitian matrix. Our findings further reveal that the total number of constraints may reduce in the presence of unitary and antiunitary symmetries. Additionally, we draw generic conclusions for the low-energy dispersion of the EPs. Based on our calculations, we show that in odd dimensions the presence of sublattice or pseudo-chiral symmetry enforces $n$th order EPs to disperse with the $(n-1)$th root. For two-, three- and four-band systems, we explicitly present the constraints needed for the occurrence of EPs in terms of system parameters and classify EPs based on their low-energy dispersion relations.

16+5 Pages, 4 Figures

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• Braid Protected Topological Band Structures with Unpaired Exceptional Points
• Symmetry-protected exceptional and nodal points in non-Hermitian systems
• Bound states and photon emission in non-Hermitian nanophotonics
• Enhanced eigenvector sensitivity and algebraic classification of sublattice-symmetric exceptional points
• Non-Hermitian eigenvalue knots and their isotopic equivalence
• Symmetry protected exceptional points of interacting fermions
• Quantum Metric Unveils Defect Freezing in Non-Hermitian Systems
• Topological superconductivity enhanced by exceptional points
• Protection of all nondefective twofold degeneracies by anti-unitary symmetries in non-Hermitian systems
• Graph theory approach to exceptional points in wave scattering