A Minimal Active-Particle Realization of Non-Hermitian Chern Bulk-Boundary Correspondence

Abstract

We show that a minimal frustrated Vicsek--Kuramoto active-particle model realizes a non-Hermitian Chern bulk-boundary correspondence. A Sakaguchi-type phase lag in the local heading alignment generates finite-wavenumber bulk instabilities and, under collision boundaries, robust one-way boundary flow. The organizing principle is a nonlinear saturation ansatz: the linearized hydrodynamic operator selects the unstable wavelength and spectral topology, while nonlinear particle dynamics saturates the selected mode. The isotropic continuum spectrum compactifies the wave-number plane and supports spectral projectors with Chern numbers $C=\pm2$, fixed by the spin structure of the dispersion matrix. Strip spectral flow then predicts chiral edge propagation, in agreement with particle simulations in the nontrivial sectors.