Real-space spectral functions of three-dimensional billion-size topological non-Hermitian matter with tensor networks

Abstract:Non-Hermitian systems host unconventional topological phenomena, while real-space spectral calculations in three dimensions remain computationally challenging. Here, we develop a tensor-network framework that combines a quantics-based matrix-product-operator representation of large real-space tight-binding Hamiltonians with a non-Hermitian kernel polynomial method. The Hermitized spectral problem is retained within the compact tensor-network representation, enabling real-space spectral function calculations for systems exceeding one billion lattice sites. Using this approach, we investigate a three-dimensional non-Hermitian higher-order topological insulator and resolve its corner-mode spectral response on a billion-site lattice, demonstrating the scalability and computational reach of the method. By tuning the gain--loss strength, we identify distinct in-gap corner-mode features in the weak- and strong-gain--loss regimes. Our results establish a scalable tensor-network framework for real-space spectral calculations in exceptionally large non-Hermitian lattice systems.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)

arXiv:2606.16424 [cond-mat.mes-hall]

(or arXiv:2606.16424v3 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2606.16424 Focus to learn more arXiv-issued DOI via DataCite

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