Supercharging exceptional points: Full-spectrum pairwise coalescence in non-Hermitian systems
Phys. Rev. A 113, 012222 – Published 20 January, 2026
DOI: https://doi.org/10.1103/7k75-b88l
Abstract
We consider non-Hermitian tight-binding one-dimensional Hamiltonians and show that imposing a certain symmetry causes all eigenvalues to pair up and the corresponding eigenstates to coalesce in pairs. This pairwise coalescence (PC) is an enhanced version of an exceptional point—the complete spectrum pairs up, not just one pair of eigenstates. The symmetry is that of reflection excluding the central two sites, and allowing flipping of nonreciprocal hoppings (“generalized off-center reflection symmetry”). Two simple examples of PC exist in the literature—our construction encompasses these examples and extends them to a vast class of Hamiltonians. We study several families of such Hamiltonians, extend to cases of full-spectrum higher-order coalescences, and show how the PC point corresponds to amplified nonorthogonality of the eigenstates and enhanced loss of norm in time evolution.
