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

Abstract:Non-Hermitian systems host a wide range of unconventional topological phenomena while large-scale simulations in finite three dimensional systems remain challenging because of the rapidly growing number of sites. In particular, higher-order topological corner modes are often studied only in small lattices, where strong finite-size effects can mask their intrinsic behavior. Here, we develop a tensor-network framework that combines quantics tensor cross interpolation with the kernel polynomial method, enabling compact representations of large non-Hermitian tight-binding Hamiltonians and direct calculations of real-space spectral functions for systems exceeding one billion lattice sites. Using this approach, we investigate three-dimensional non-Hermitian higher-order topological insulators with with structured real-space geometries. The unprecedented system size enables direct access to the macroscopic regime and allows corner-mode spectral responses to be resolved in genuinely three-dimensional systems. By tuning the loss strength, we identify distinct in-gap corner modes across weak- and strong-loss regimes. Our results establish tensor-network algorithms as a powerful strategy to perform real-space spectral calculations in exceptionally large non-Hermitian systems.

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

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

(or arXiv:2606.16424v2 [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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