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arXiv · 2607.24496

Bulk spectra and the non-Hermitian skin effect in systems with long-range couplings

Jonathan Sturm·Pia Kreß·Adriana Pálffy
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Abstract

To achieve translational symmetry for the computation of the band structure of a lattice model, one can either consider an infinite lattice or impose periodic boundary conditions (PBC). While in systems with short-range couplings these two approaches are equivalent, we show that for long-range couplings one can obtain considerably different results. We compare the two methods on the basis of one-dimensional quantum emitter chains both in free space and when coupled to a waveguide. The latter system allows for asymmetric couplings enabling the non-Hermitian skin effect, which we analyze using the two different band-structure calculation methods. We find that only PBC lead to physically and mathematically robust results, while the infinite-chain approach entails convergence issues and is unable to satisfyingly explain the emergence of the non-Hermitian skin effect in the waveguide system. Using PBC reveals unusual findings like a non-star shaped generalized Brillouin zone and strongly localized eigenstates with zero winding number.

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Jonathan Sturm, Pia Kreß, Adriana Pálffy. 2026-07-27. Bulk spectra and the non-Hermitian skin effect in systems with long-range couplings. https://arxiv.org/abs/2607.24496

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