Self-consistent tensor network method for correlated super-moiré matter beyond one billion sites
arXiv:2503.04373 · doi:10.1103/krjp-mn4v
Abstract
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 for interacting systems. Here, 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. Our method combines a tensor-network kernel polynomial method with quantics tensor cross interpolation algorithm, enabling us to solve exponentially large models, including those whose single particle Hamiltonian is too large to be stored explicitly. 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. Our methodology provides a strategy to solve exceptionally large interacting problems, providing a widely applicable strategy to compute correlated super-moiré quantum matter.
arXiv comment16 pages, 9 figures
References in corpus (66)
- Advanced capabilities for materials modelling with Quantum ESPRESSO
- Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
- The density-matrix renormalization group in the age of matrix product states
- The density-matrix renormalization group
- Tuning superconductivity in twisted bilayer graphene
- Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
- Intrinsic quantized anomalous Hall effect in a moiré heterostructure
- Spin Liquid Ground State of the Kagome Heisenberg Model
- Emergence of magnetism in graphene materials and nanostructures
- The Kernel Polynomial Method
- The ITensor Software Library for Tensor Network Calculations
- Tunable Phase Boundaries and Ultra-Strong Coupling Superconductivity in Mirror Symmetric Magic-Angle Trilayer Graphene
- Time-dependent variational principle for quantum lattices
- Magnetism in graphene nano-islands
- Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
- Time-evolution methods for matrix-product states
- Tensor networks for complex quantum systems
- Integer and fractional Chern insulators in twisted bilayer MoTe2
- Localization and delocalization of light in photonic moire lattices
- Spin liquid phase of the Heisenberg model on the triangular lattice
- Unsupervised Generative Modeling Using Matrix Product States
- Optical soliton formation controlled by angle twisting in photonic moiré lattices
- Superconductivity in the Hubbard model and its interplay with charge stripes and next-nearest hopping t'
- Effective Extensible Programming: Unleashing Julia on GPUs
- What limits the simulation of quantum computers?
- Electrically controllable magnetism in twisted bilayer graphene
- Superconductivity and strong interactions in a tunable moiré quasiperiodic crystal
- Atomic Bose-Einstein condensate in a twisted-bilayer optical lattice
- Coexistence of superconductivity with partially filled stripes in the Hubbard model
- Chebyshev matrix product state approach for spectral functions
- Gate-tunable heavy fermions in a moiré Kondo lattice
- A Quantum Inspired Approach to Exploit Turbulence Structures
- Critical delocalization of chiral zero energy modes in graphene
- Programming moiré patterns in 2D materials by bending
- Cold atoms in twisted bilayer optical potentials
- Learning Feynman Diagrams with Tensor Trains
- Emulating heavy fermions in twisted trilayer graphene
- Imaging inter-valley coherent order in magic-angle twisted trilayer graphene
- Simulating twistronics without a twist
- Electrical switching of a moiré ferroelectric superconductor
- Quantics Tensor Cross Interpolation for High-Resolution, Parsimonious Representations of Multivariate Functions in Physics and Beyond
- Multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains
- Effect of charged line defects on conductivity in graphene: numerical Kubo and analytical Boltzmann approaches
- Observation of linear and nonlinear light localization at the edges of moiré lattices
- Supermoiré low-energy effective theory of twisted trilayer graphene
- Learning tensor networks with tensor cross interpolation: new algorithms and libraries
- Topological spin excitations in non-Hermitian spin chains with a generalized kernel polynomial algorithm
- Complete quantum-inspired framework for computational fluid dynamics
- Symmetry breaking and anomalous conductivity in a double moiré superlattice
- Topological spin excitations in Harper-Heisenberg spin chains
- A Tensor Train Continuous Time Solver for Quantum Impurity Models
- Observing the two-dimensional Bose glass in an optical quasicrystal
- Tensor networks enable the calculation of turbulence probability distributions
- Probing thermalization through spectral analysis with matrix product operators
- Designing topology and fractionalization in narrow gap semiconductor films via electrostatic engineering
- High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin-orbit effects and p-wave superconductivity
- Inducing a many-body topological state of matter through Coulomb-engineered local interactions
- Cross-extrapolation reconstruction of low-rank functions and application to quantum many-body observables in the strong coupling regime
- Compactness of quantics tensor train representations of local imaginary-time propagators
- Simulating the quantum Fourier transform, Grover's algorithm, and the quantum counting algorithm with limited entanglement using tensor-networks
- Magnetic Bloch States at Integer Flux Quanta Induced by Super-moiré Potential in Graphene Aligned with Twisted Boron Nitride
- Plasmonic Waveguides from Coulomb-Engineered Two-Dimensional Metals
- Tensorized orbitals for computational chemistry
- Many-body Liouvillian dynamics with a non-Hermitian tensor-network kernel polynomial algorithm
- Correlated states in super-moiré materials with a kernel polynomial quantics tensor cross interpolation algorithm
- Fully numerical Hartree-Fock calculations for atoms and small molecules with quantics tensor trains