# Artificial intelligence for artificial materials: moir'e atom

arXiv: https://arxiv.org/abs/2303.08162 · HTML: https://mlsanity.com/paper/2303.08162/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 78 references that are in the map.
- First posted on arXiv 14 Mar 2023.

## Builds on (most cited first, 17 of 17)

- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [Deep autoregressive models for the efficient variational simulation of many-body quantum systems](https://mlsanity.com/paper/1902.04057/) (2019)
- [Quantum Entanglement in Deep Learning Architectures](https://mlsanity.com/paper/1803.09780/) (2018)
- [Neural-Network Quantum States, String-Bond States, and Chiral Topological States](https://mlsanity.com/paper/1710.04045/) (2017)
- [Gauge equivariant neural networks for quantum lattice gauge theories](https://mlsanity.com/paper/2012.05232/) (2020)
- [Discovering Quantum Phase Transitions with Fermionic Neural Networks](https://mlsanity.com/paper/2202.05183/) (2022)
- [Solving the electronic Schr"odinger equation for multiple nuclear geometries with weight-sharing deep neural networks](https://mlsanity.com/paper/2105.08351/) (2021)
- [Neural tensor contractions and the expressive power of deep neural quantum states](https://mlsanity.com/paper/2103.10293/) (2021)
- [Electronic excited states in deep variational Monte Carlo](https://mlsanity.com/paper/2203.09472/) (2022)
- [Ab-initio study of interacting fermions at finite temperature with neural canonical transformation](https://mlsanity.com/paper/2105.08644/) (2021)
- [Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum states](https://mlsanity.com/paper/2008.00118/) (2020)
- [Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulation](https://mlsanity.com/paper/2211.03198/) (2022)
- [Simulating 2+1D Lattice Quantum Electrodynamics at Finite Density with Neural Flow Wavefunctions](https://mlsanity.com/paper/2212.06835/) (2022)
- [Spacetime Neural Network for High Dimensional Quantum Dynamics](https://mlsanity.com/paper/2108.02200/) (2021)
- [Infinite Neural Network Quantum States: Entanglement and Training Dynamics](https://mlsanity.com/paper/2112.00723/) (2021)

## Built on by (most cited first, 1 of 1)

- [Pairing-based graph neural network for simulating quantum materials](https://mlsanity.com/paper/2311.02143/) (2023)

## Abstract (arXiv)

Moir'e engineering in atomically thin van der Waals heterostructures creates artificial quantum materials with designer properties. We solve the many-body problem of interacting electrons confined to a moir'e superlattice potential minimum (the moir'e atom) using a 2D fermionic neural network. We show that strong Coulomb interactions in combination with the anisotropic moir'e potential lead to striking ``Wigner molecule" charge density distributions observable with scanning tunneling microscopy.