Machine-learning semi-local density functional theory for many-body lattice models at zero and finite temperature

Abstract

We introduce a machine-learning density-functional-theory formalism for the spinless Hubbard model in one dimension at both zero and finite temperature. In the zero-temperature case this establishes a one-to-one relation between the site occupation and the total energy, which is then minimised at the ground-state occupation. In contrast, at finite temperature the same relation is defined between the Helmholtz free energy and the equilibrium site occupation. Most importantly, both functionals are semi-local, so that they are independent from the size of the system under investigation and can be constructed over exact data for small systems. These 'exact' functionals are numerically defined by neural networks. We also define additional neural networks for finite-temperature thermodynamical quantities, such as the entropy and heat capacity. These can be either a functional of the ground-state site occupation or of the finite-temperature equilibrium site occupation. In the first case their equilibrium value does not correspond to an extremal point of the functional, while it does in the second case. Our work gives us access to finite-temperature properties of many-body systems in the thermodynamic limit.

References in corpus (24)

• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Machine learning and the physical sciences
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Continuous-time Monte Carlo methods for quantum impurity models
• Machine learning phases of matter
• By-passing the Kohn-Sham equations with machine learning
• Finding Density Functionals with Machine Learning
• Identifying topological order through unsupervised machine learning
• A deep learning approach to identify local structures in atomic-resolution transmission electron microscopy images
• Deep learning and the Schrödinger equation
• Unsupervised machine learning account of magnetic transitions in the Hubbard model
• Solving the Bose-Hubbard model with machine learning
• Deep Learning and Density Functional Theory
• NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
• 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
• Predicting the Curie temperature of ferromagnets using machine learning
• Deep learning the Hohenberg-Kohn maps of Density Functional Theory
• A Bayesian approach to NMR crystal structure determination
• Extensive deep neural networks for transferring small scale learning to large scale systems
• Machine learning density functional theory for the Hubbard model
• Deep neural networks for direct, featureless learning through observation: the case of 2d spin models
• Machine learning electron correlation in a disordered medium
• Uniqueness of density-to-potential mapping for fermionic lattice systems