Fragmented exceptional points and their bulk and edge realizations in lattice models

Abstract

Exceptional points (EPs) are spectral defects displayed by non-Hermitian systems in which multiple degenerate eigenvalues share a single eigenvector. This distinctive feature makes systems exhibiting EPs more sensitive to external perturbations than their Hermitian counterparts, where degeneracies are nondefective diabolic points. In contrast to these widely studied cases, more complex non-Hermitian degeneracies in which the eigenvectors are only partially degenerate are poorly understood. Here, we characterize these fragmented exceptional points (FEPs) systematically from a physical perspective, and demonstrate how they can be induced into the bulk and edge spectrum of two-dimensional and three-dimensional lattice models, exemplified by non-Hermitian versions of a Lieb lattice and a higher-order topological Dirac semimetal. The design of the systems is facilitated by an efficient algebraic approach within which we provide precise conditions for FEPs that can be evaluated directly from a given model Hamiltonian. The free design of FEPs significantly opens up a new frontier for non-Hermitian physics and expands the scope for designing systems with unconventional response characteristics.

27 pages, 13 figures

References in corpus (16)

• The physics of exceptional points
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Topological Semimetals
• Observation of a localized flat-band state in a photonic Lieb lattice
• Observation of bound states in Lieb photonic lattices
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Topological Insulators on the Lieb and Perovskite Lattices
• Topological Phases for Fermionic Cold Atoms on the Lieb Lattice
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Higher-Order Weyl Semimetals
• Flat bands and nontrivial topological properties in an extended Lieb lattice
• Linear response theory of open systems with exceptional points
• From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
• Response strengths of open systems at exceptional points

Cited by in corpus (2)

• A non-Hermitian Su-Schrieffer-Heeger model with the energy levels of free parafermions
• Multi-block exceptional points in open quantum systems