Tensor-network methodology for super-moiré excitons beyond one billion sites

• URL: http://arxiv.org/abs/2603.02011v1
• Date: Mon, 02 Mar 2026 15:57:10 GMT
• Title: Tensor-network methodology for super-moiré excitons beyond one billion sites
• Authors: Anouar Moustaj, Yitao Sun, Tiago V. C. Antão, Lumen Eek, Jose L. Lado,
• Abstract summary: We show a tensor-network method for the real-space Bethe-Salpeter Hamiltonian.<n>We demonstrate our methodology for one- and two-dimensional super-moiré systems.<n>Our results establish a real-space methodology enabling the simulation of excitonic physics in large-scale quasicrystal and super-moiré quantum matter.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Computing excitonic spectra in quasicrystal and super-moiré systems constitutes a formidable challenge due to the exceptional size of the excitonic Hilbert space. Here, we demonstrate a tensor-network method for the real-space Bethe-Salpeter Hamiltonian, allowing us to access the spectra of an excitonic $10^{18}$-dimensional Hamiltonian, and enabling the direct computation of bound-exciton spectral functions for systems exceeding one billion lattice sites, several orders of magnitude beyond the capabilities of conventional approaches. Our method combines a tensor-network encoding of the real-space Bethe-Salpeter Hamiltonian with a Chebyshev tensor network algorithm. This strategy bypasses explicit storage of the Hamiltonian while preserving full real-space resolution across widely different length scales. We demonstrate our methodology for one- and two-dimensional super-moiré systems, achieving the simultaneous resolution of atomistic and mesoscopic structures in the excitonic spectra in billion-size systems, showing exciton miniband formation and moiré-induced spatial confinement. Our results establish a real-space methodology enabling the simulation of excitonic physics in large-scale quasicrystal and super-moiré quantum matter.

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