Backflow Transformations via Neural Networks for Quantum Many-Body Wave-Functions

Abstract

Obtaining an accurate ground state wave function is one of the great challenges in the quantum many-body problem. In this paper, we propose a new class of wave functions, neural network backflow (NNB). The backflow approach, pioneered originally by Feynman, adds correlation to a mean-field ground state by transforming the single-particle orbitals in a configuration-dependent way. NNB uses a feed-forward neural network to find the optimal transformation. NNB directly dresses a mean-field state, can be systematically improved and directly alters the sign structure of the wave-function. It generalizes the standard backflow which we show how to explicitly represent as a NNB. We benchmark the NNB on a Hubbard model at intermediate doping finding that it significantly decreases the relative error, restores the symmetry of both observables and single-particle orbitals, and decreases the double-occupancy density. Finally, we illustrate interesting patterns in the weights and bias of the optimized neural network.

References in corpus (46)

• An overview of gradient descent optimization algorithms
• Efficient classical simulation of slightly entangled quantum computations
• Empirical Evaluation of Rectified Activations in Convolutional Network
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Entanglement renormalization
• Many-body quantum state tomography with neural networks
• Criticality, the area law, and the computational power of PEPS
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Quantum Entanglement in Neural Network States
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Machine Learning Topological States
• Symmetries and many-body excited states with neural-network quantum states
• Equivalence of restricted Boltzmann machines and tensor network states
• Inhomogeneous backflow transformations in quantum Monte Carlo calculations
• Effects of Backflow Correlation in the Three-Dimensional Electron Gas: Quantum Monte Carlo Study
• Approximating quantum many-body wave-functions using artificial neural networks
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Constructing exact representations of quantum many-body systems with deep neural networks
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• Backflow Correlations for the Electron Gas and Metallic Hydrogen
• Machine learning technique to find quantum many-body ground states of bosons on a lattice
• Role of backflow correlations for the non-magnetic phase of the t-t' Hubbard model
• Solving frustrated quantum many-particle models with convolutional neural networks
• Ground-State Properties of Quantum Many-Body Systems: Entangled-Plaquette States and Variational Monte Carlo
• Chiral Topological Phases from Artificial Neural Networks
• Complete-Graph Tensor Network States: A New Fermionic Wave Function Ansatz for Molecules
• Learning hard quantum distributions with variational autoencoders
• Backflow correlations in the Hubbard model: an efficient tool for the metal-insulator transition and the large-U limit
• Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks
• Spin-liquid and magnetic phases in the anisotropic triangular lattice: the case of $\kappa$-(ET)${}_2$X
• Efficient Representation of Topologically Ordered States with Restricted Boltzmann Machines
• Iterative backflow renormalization procedure for many-body ground state wave functions of strongly interacting normal Fermi liquids
• Nonlinear Network description for many-body quantum systems in continuous space
• Neural-network states for the classical simulation of quantum computing
• Method to solve quantum few-body problems with artificial neural networks
• Quantum Monte Carlo study of the Ne atom and the Ne+ ion
• Variational ground states of 2D antiferromagnets in the valence bond basis
• Striped spin liquid crystal ground state instability of kagome antiferromagnets
• Generalized Transfer Matrix States from Artificial Neural Networks
• Many-body wavefunctions for normal liquid ${}^3$He
• The itinerant ferromagnetic phase of the Hubbard model
• Variational optimization in the AI era: Computational Graph States and Supervised Wave-function Optimization
• Metal-insulator transition and strong-coupling spin liquid in the $t-t^{\prime }$ Hubbard model
• Interaction induced Fermi-surface renormalization in the $t_1-t_2$ Hubbard model close to the Mott-Hubbard transition

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