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.
Related
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BibTeX
@misc{sun2026realspace,
title = {{Real-space spectral functions of three-dimensional billion-size topological non-Hermitian matter with tensor networks}},
author = {Yitao Sun and Jose L. Lado and Guangze Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.16424},
eprint = {2606.16424},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.16424},
}
RIS
TY - UNPB
TI - Real-space spectral functions of three-dimensional billion-size topological non-Hermitian matter with tensor networks
AU - Yitao Sun
AU - Jose L. Lado
AU - Guangze Chen
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2606.16424
UR - https://arxiv.org/abs/2606.16424
AB - 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.
ER -