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

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. While in sys- tems 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 periodic boundary conditions 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. In addition, the waveguide system yields unusual findings like a non-star shaped generalized Brillouin zone and strongly localized eigenstates with zero winding number.

arXiv:2607.24496 [quant-ph]

(or arXiv:2607.24496v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.24496 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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