In the study of electronic structure, the wave function view dominates the current research landscape and forms the theoretical foundation of modern quantum mechanics. In contrast, valence bond (VB) theory represents chemical bonds as shared electron pairs and can provide an intuitive, particle-based insight into chemical bonding. In this work, using a newly developed periodic dynamic Voronoi Metropolis sampling (PDVMS) method, we project classical many-body electronic configurations from the neural network wave function and apply VB theory to construct a complementary particle-view paradigm. The powerful neural network wave function can achieve near-exact solutions for the ground state of both molecular and solid systems. It allows us to definitively characterize the ground state of benzene by reassessing the competition between its two VB structures. Extending PDVMS to solids, we also predict a spin-staggered VB structure in graphene, which explains emergent magnetic properties in graphene-based nanostructures. Furthermore, this particle view provides insight into the optimization process of the neural network wave function itself. Our work thus introduces a framework for analyzing many-body electronic structure in molecules and solids, opening new avenues for investigating this complex problem and its associated exotic phenomena.
In the study of electronic structure, the wave function view dominates the current research landscape and forms the theoretical foundation of modern quantum mechanics. In contrast, valence bond (VB) theory represents chemical bonds as shared electron pairs and can provide an intuitive, particle-based insight into chemical bonding. In this work, using a newly developed periodic dynamic Voronoi Metropolis sampling (PDVMS) method, we project classical many-body electronic configurations from the neural network wave function and apply VB theory to construct a complementary particle-view paradigm. The powerful neural network wave function can achieve near-exact solutions for the ground state of both molecular and solid systems. It allows us to definitively characterize the ground state of benzene by reassessing the competition between its two VB structures. Extending PDVMS to solids, we also predict a spin-staggered VB structure in graphene, which explains emergent magnetic properties in graphene-based nanostructures. Furthermore, this particle view provides insight into the optimization process of the neural network wave function itself. Our work thus introduces a framework for analyzing many-body electronic structure in molecules and solids, opening new avenues for investigating this complex problem and its associated exotic phenomena.
Given access to accurate solutions of the many-electron Schrödinger equation, nearly all chemistry could be derived from first principles.Exact wave functions of interesting chemical systems are out of reach because they are NP-hard to compute in general, but approximations can be found using polynomially scaling algorithms.The key challenge for many of these algorithms is the choice of wave function approximation, or Ansatz, which must trade off between efficiency and accuracy.Neural networks have shown impressive power as accurate practical function approximators and promise as a compact wave-function Ansatz for spin systems, but problems in electronic structure require wave functions that obey Fermi-Dirac statistics.Here we introduce a novel deep learning architecture, the Fermionic neural network, as a powerful wave-function Ansatz for many-electron systems.The Fermionic neural network is able to achieve accuracy beyond other variational quantum Monte Carlo Ansatz on a variety of atoms and small molecules.Using no data other than atomic positions and charges, we predict the dissociation curves of the nitrogen molecule and hydrogen chain, two challenging strongly correlated systems, to significantly higher accuracy than the coupled cluster method, widely considered the most accurate scalable method for quantum chemistry at equilibrium geometry.This demonstrates that deep neural networks can improve the accuracy of variational quantum Monte Carlo to the point where it outperforms other ab initio quantum chemistry methods, opening the possibility of accurate direct optimization of wave functions for previously intractable many-electron systems.
Carleo and Troyer [3] have recently pointed out the possibility of solving quantum many-body problems by using Artificial Neural Networks (ANN). Their work is based on minimizing a variational wave function to obtain the ground states for various spin-dependent systems. This work is primarily focused on developing efficient method using ANN to solve the ground state wave function for atomic systems. We have developed a theoretical groundwork to represent the wave function of a many-electron atom by using artificial neural network while still preserving its antisymmetric property. By using the Metropolis algorithm, Variational Monte Carlo (VMC), and Stochastic Reconfiguration (SR) methods for minimization, we were able to obtain a highly accurate ground state wave function for the He atom. To verify our optimization algorithm, we reproduced the results for the ground state of a three dimensional Simple Harmonic Oscillator (SHO) given by Teng [18].
Neural-network quantum states have been successfully used to study a variety of lattice and continuous-space problems. Despite a great deal of general methodological developments, representing fermionic matter is however still early research activity. Here we present an extension of neural-network quantum states to model interacting fermionic problems. Borrowing techniques from quantum simulation, we directly map fermionic degrees of freedom to spin ones, and then use neural-network quantum states to perform electronic structure calculations. For several diatomic molecules in a minimal basis set, we benchmark our approach against widely used coupled cluster methods, as well as many-body variational states. On some test molecules, we systematically improve upon coupled cluster methods and Jastrow wave functions, reaching chemical accuracy or better. Finally, we discuss routes for future developments and improvements of the methods presented.
We design a neural network Ansatz for variationally finding the ground-state wave function of the Homogeneous Electron Gas, a fundamental model in the physics of extended systems of interacting fermions. We study the spin-polarised and paramagnetic phases with 7, 14 and 19 electrons over a broad range of densities from rs=1 to rs=100, obtaining similar or higher accuracy compared to a state-of-the-art iterative backflow baseline even in the challenging regime of very strong correlation. Our work extends previous applications of neural network Ansätze to molecular systems with methods for handling periodic boundary conditions, and makes two notable changes to improve performance: splitting the pairwise streams by spin alignment and generating backflow coordinates for the orbitals from the network. We illustrate the advantage of our high quality wave functions in computing the reduced single particle density matrix. This contribution establishes neural network models as flexible and high precision Ansätze for periodic electronic systems, an important step towards applications to crystalline solids.
Abstract Moiré systems have emerged as an exciting new tunable platform for engineering and probing quantum matter. A large number of exotic states have been observed, stimulating intense efforts in experiment, theory, and simulation. Utilizing a neural-network-based quantum Monte Carlo approach, we discover a new ground state of the two-dimensional electron gas in a honeycomb moiré potential at a filling factor of ν m = 1/4 (one electron every four moiré minima). In this state, two opposite-spin electrons pair to form singlet-like valence bond states which restore local C 6 symmetry in hexagonal molecules each spanning 6 moiré minima. These molecules of pairs then form a molecular Wigner crystal, leaving one quarter of the moiré minima mostly depleted. The formation of such a paired Wigner crystal, absent any confining potential or attractive interaction to facilitate "pre-assembling" the molecule, provides a fascinating case of collective phenomena in strongly interacting quantum many-body systems and opportunities to engineer exotic properties in a system within current experimental setups. This discovery signals a new level of predictive power in quantum many-body computations enabled by neural networks and machine learning.