Speaker
Description
Moiré and super-moiré materials provide exceptional platforms to engineer exotic correlated quantum matter. The vast number of sites required to model moiré systems in real space remains a formidable challenge due to the immense computational resources required. Super-moiré materials push this requirement to the limit, where millions or even billions of sites need to be considered, a requirement beyond the capabilities of conventional methods. Here, we establish methodologies [1,2,3] to solve exponentially large single particle problems using many-body tensor networks. This enables us to solve exponentially large lattice models, including those whose single-particle Hamiltonian is too large to be stored explicitly. First [1], we show that tensor network algorithms allow performing time-evolution of non-linear dynamics, where we reach system sizes of one trillion sites. Second [2], we establish a methodology that allows solving correlated states in systems reaching a billion sites, that exploits tensor-network representations of real-space Hamiltonians and self-consistent real-space mean-field equations. We demonstrate our methodology with super-moiré systems featuring spatially modulated hoppings, many-body interactions, and domain walls, showing that it allows access to self-consistent symmetry broken states and spectral functions of real-space models reaching a billion sites. Finally [3], we demonstrate a method to compute local topological invariants of exceptionally large systems using tensor networks, enabling the computation of invariants for Hamiltonians with hundreds of millions of sites. Our approach leverages a tensor-network representation of the density matrix using a Chebyshev tensor network algorithm, enabling large-scale calculations of topological markers in quasicrystalline and moire systems. Our methodology establishes strategies to solve exceptionally large single-particle problems with quantum many-body algorithms, providing a widely applicable strategy to compute topological and correlated super-moiré quantum matter.
[1] Marcel Niedermeier, Adrien Moulinas, Thibaud Louvet, Jose L. Lado, Xavier Waintal, Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation, arXiv:2507.04262 (2025)
[2] Yitao Sun, Marcel Niedermeier, Tiago V. C. Antão, Adolfo O. Fumega, Jose L. Lado, Self-consistent tensor network method for correlated super-moiré matter beyond one billion sites, arXiv:2503.04373 (2025)
[3] Tiago V. C. Antão, Yitao Sun, Adolfo O. Fumega, Jose L. Lado, Tensor network method for real-space topology in quasicrystal Chern mosaics, arXiv:2506.05230 (2025)
