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Tensor network approach to momentum-resolved spectroscopy in nonperiodic super-moiré systems

Anouar Moustaj*, Yitao Sun, Tiago V. C. Antão, and Jose L. Lado

  • *Contact author: anouar.moustaj@aalto.fi
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Phys. Rev. Research 8, 023282 – Published 11 June, 2026

DOI: https://doi.org/10.1103/9btt-y8sh

Abstract

Computing spectral functions in large, nonperiodic super-moiré systems remains an open problem due to the exceptionally large system size that must be considered. Here, we establish a tensor network methodology that allows computing momentum-resolved spectral functions of noninteracting and interacting super-moiré systems at an atomistic level. Our methodology relies on encoding an exponentially large tight-binding problem as an auxiliary quantum many-body problem, solved with a many-body kernel polynomial tensor network algorithm combined with a quantum Fourier transform tensor network. We demonstrate the method for one- and two-dimensional super-moiré systems, including super-moiré with nonuniform strain, interactions treated at the mean-field level, and quasicrystalline super-moiré patterns. Furthermore, we demonstrate that our methodology allows us to compute momentum-resolved spectral functions restricted to selected regions of a super-moiré, enabling direct imaging of position-dependent electronic structure and minigaps in super-moiré systems with nonuniform strain. Our results establish a powerful methodology to compute momentum-resolved spectral functions in exceptionally large super-moiré systems, providing a tool to directly model quantum twisting microscope experiments in twisted van der Waals heterostructures.

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Phys. Rev. Research 8, 023282– Published 11 June, 2026
  • Received 30 December 2025
  • Accepted 10 May 2026
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