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arXiv:2606.16424

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

Yitao Sun, Jose L. Lado, Guangze Chen

cond-mat.mes-hallquant-phSubmitted Jun 15, 2026• Announced Jun 16, 2026• 0 citations• Revised Oct 17, 2026 (v3)
v1 · Jun 15, 2026v2 · Jun 16, 2026v3 · Oct 17, 2026
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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.

Comments
17 pages, 13 figures

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