Real-space spectral functions of three-dimensional billion-size topological non-Hermitian matter with tensor networks
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Sun, Yitao, Lado, Jose L., Chen, Guangze
Institutions: Aalto University, Chalmers University of Technology
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7164889676