Year: 2025
Type: preprint
Abstract: The Chebyshev expansion method is a well-established technique for computing the time evolution of quantum states, particularly in Hermitian systems with a bounded spectrum. Here, we show that the applicability of the Chebyshev expansion method extends well beyond this constraint: It remains valid across the entire complex plane and is thus suitable for arbitrary non-Hermitian matrices. We identify that numerical rounding errors are the primary source of errors encountered when applying the method outside the conventional spectral bounds, and they are not caused by fundamental limitations. By carefully selecting the spectral radius and the time step, we show how these errors can be effectively suppressed, enabling accurate time evolution calculations in non-Hermitian systems. We derive an analytic upper bound for the rounding error, which serves as a practical guideline for selecting time steps in numerical simulations. As an application, we illustrate the performance of the method by computing the time evolution of wave packets in the Hatano-Nelson model.
Source: arXiv (Cornell University)
DOI: 10.1103/nbxh-j277
Authors: Holló, Áron, Varjas, Dániel, Fulga, Cosma, Oroszlány, László, Könye, Viktor
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1053465433, G1804794778, G1863392119, G1867225360, G2044776484, G206414428, G2148593763, G2152757567, G285949800, G3059208328, G3681588884, G3764250195, G4568777066, G4833133300, The Trilateral Magnetic Exchange, G5553879734, G5945661640, G6417321272, EXC 2147: Komplexität und Topologie in Quantenmaterialien (CT.QMAT), G675428594, G765612021, G8214616130
OpenAlex ID: W7091187930
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