Deep learning the Hohenberg-Kohn maps of Density Functional Theory

Abstract

A striking consequence of the Hohenberg-Kohn theorem of density functional theory is the existence of a bijection between the local density and the ground-state many-body wave function. Here we study the problem of constructing approximations to the Hohenberg-Kohn map using a statistical learning approach. Using supervised deep learning with synthetic data, we show that this map can be accurately constructed for a chain of one-dimensional interacting spinless fermions, in different phases of this model including the charge ordered Mott insulator and metallic phases and the critical point separating them. However, we also find that the learning is less effective across quantum phase transitions, suggesting an intrinsic difficulty in efficiently learning non-smooth functional relations. We further study the problem of directly reconstructing complex observables from simple local density measurements, proposing a scheme amenable to statistical learning from experimental data.

References in corpus (22)

• Many-Body Physics with Ultracold Gases
• Machine learning and the physical sciences
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Localization and delocalization errors in density functional theory and implications for band-gap prediction
• By-passing the Kohn-Sham equations with machine learning
• Finding Density Functionals with Machine Learning
• Generation and manipulation of Schrödinger cat states in Rydberg atom arrays
• Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator
• A Bose-Einstein condensate in a random potential
• Strongly interacting bosons in a disordered optical lattice
• Orbital-free Bond Breaking via Machine Learning
• Deep Learning and Density Functional Theory
• Emerging 2D Gauge theories in Rydberg configurable arrays
• Pure density functional for strong correlations and the thermodynamic limit from machine learning
• Machine Learning the Physical Non-Local Exchange-Correlation Functional of Density-Functional Theory
• Neural-network Kohn-Sham exchange-correlation potential and its out-of-training transferability
• Kinetic energy densities based on the fourth order gradient expansion: performance in different classes of materials and improvement via machine learning
• Numerical renormalization group study of the correlation functions of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg chain
• Non-Equilibrium Mass Transport in the 1D Fermi-Hubbard Model
• Machine learning density functional theory for the Hubbard model
• Supervised machine learning of ultracold atoms with speckle disorder

Cited by in corpus (34)

• Machine Learning in Nuclear Physics
• Provably efficient machine learning for quantum many-body problems
• Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics
• Quantum Machine Learning for Chemistry and Physics
• Quantum deep field: data-driven wave function, electron density generation, and atomization energy prediction and extrapolation with machine learning
• Nuclear energy density functionals from machine learning
• Improved machine learning algorithm for predicting ground state properties
• Quantum Phase Recognition via Quantum Kernel Methods
• Machine learning the derivative discontinuity of density-functional theory
• Density Functional Theory Transformed into a One-electron Reduced Density Matrix Functional Theory for the Capture of Static Correlation
• Deep Learning the Functional Renormalization Group
• Scalable neural networks for the efficient learning of disordered quantum systems
• Comparison of Density-Matrix Corrections to Density Functional Theory
• Machine Learning Universal Bosonic Functionals
• Building Kohn-Sham potentials for ground and excited states
• Efficient Learning of a One-dimensional Density Functional Theory
• Calibration of nuclear charge density distribution by back-propagation neural networks
• Machine learning band gaps from the electron density
• A Kohn-Sham Scheme Based Neural Network for Nuclear Systems
• Supervised learning of few dirty bosons with variable particle number
• Neural networks in quantum many-body physics: a hands-on tutorial
• Neural-network-supported basis optimizer for the configuration interaction problem in quantum many-body clusters: Feasibility study and numerical proof
• Deep learning density functionals for gradient descent optimization
• Extracting Many-Body Quantum Resources within One-Body Reduced Density Matrix Functional Theory
• Orbital-Free Quasi-Density Functional Theory
• Learning interactions between Rydberg atoms
• The Levy-Lieb embedding of density functional theory and its Quantum Kernel: Illustration for the Hubbard Dimer using near-term quantum algorithms
• Topological Learning in Multi-Class Data Sets
• Machine-learning semi-local density functional theory for many-body lattice models at zero and finite temperature
• Solving deep-learning density functional theory via variational autoencoders
• Lies My Teacher Told Me About Density Functional Theory: Seeing Through Them with the Hubbard Dimer
• Learning Minimal Representations of Fermionic Ground States
• Global sampling of Feynman's diagrams through Normalizing Flow
• Machine learning based prediction of the electronic structure of quasi-one-dimensional materials under strain