Supercharging exceptional points: Full-spectrum pairwise coalescence in non-Hermitian systems

TL;DR

This paper introduces a symmetry-induced phenomenon called Pairwise Coalescence in non-Hermitian Hamiltonians, where all eigenvalues and eigenstates pair up, leading to full-spectrum exceptional point behavior with potential applications in wave dynamics.

Contribution

It generalizes existing exceptional point concepts by demonstrating how a specific symmetry causes complete spectrum pairing and coalescence in non-Hermitian systems, extending prior examples to a broad class of Hamiltonians.

Findings

All eigenvalues form pairs under the symmetry.

Full-spectrum coalescence leads to amplified non-orthogonality.

Enhanced loss of norm during time evolution at PC points.

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 non-reciprocal 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 non-orthogonality of the eigenstates and enhanced loss of norm in time evolution.