Recurrence method in Non-Hermitian Systems

• URL: http://arxiv.org/abs/2412.14912v1
• Date: Thu, 19 Dec 2024 14:44:42 GMT
• Title: Recurrence method in Non-Hermitian Systems
• Authors: Haoyan Chen, Yi Zhang,
• Abstract summary: We propose a novel and systematic recurrence method for the energy spectra of non-Hermitian systems under open boundary conditions. Our formalism exhibits better accuracy and performance on multi-band non-Hermitian systems than numerical diagonalization or the non-Bloch band theory. Our recurrence method offers a novel and favorable formalism to the intriguing physics of non-Hermitian systems under open boundary conditions.
• Score: 3.8601741392210434
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• Abstract: We propose a novel and systematic recurrence method for the energy spectra of non-Hermitian systems under open boundary conditions based on the recurrence relations of their characteristic polynomials. Our formalism exhibits better accuracy and performance on multi-band non-Hermitian systems than numerical diagonalization or the non-Bloch band theory. It also provides a targeted and efficient formulation for the non-Hermitian edge spectra. As demonstrations, we derive general expressions for both the bulk and edge spectra of multi-band non-Hermitian models with nearest-neighbor hopping and under open boundary conditions, such as the non-Hermitian Su-Schrieffer-Heeger and Rice-Mele models and the non-Hermitian Hofstadter butterfly - 2D lattice models in the presence of non-reciprocity and perpendicular magnetic fields, which is only made possible by the significantly lower complexity of the recurrence method. In addition, we use the recurrence method to study non-Hermitian edge physics, including the size-parity effect and the stability of the topological edge modes against boundary perturbations. Our recurrence method offers a novel and favorable formalism to the intriguing physics of non-Hermitian systems under open boundary conditions.

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