Tensor-network methodology for super-moiré excitons beyond one billion sites
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arXiv
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2026
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| _version_ | 1866915851054088192 |
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| author | Moustaj, Anouar Sun, Yitao Antão, Tiago V. C. Eek, Lumen Lado, Jose L. |
| author_facet | Moustaj, Anouar Sun, Yitao Antão, Tiago V. C. Eek, Lumen Lado, Jose L. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_02011 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tensor-network methodology for super-moiré excitons beyond one billion sites Moustaj, Anouar Sun, Yitao Antão, Tiago V. C. Eek, Lumen Lado, Jose L. Strongly Correlated Electrons Mesoscale and Nanoscale Physics Materials Science Computational Physics Quantum Physics 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. |
| title | Tensor-network methodology for super-moiré excitons beyond one billion sites |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics Materials Science Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2603.02011 |