Deep Learning-Enhanced Variational Monte Carlo Method for Quantum Many-Body Physics

Abstract

Artificial neural networks have been successfully incorporated into variational Monte Carlo method (VMC) to study quantum many-body systems. However, there have been few systematic studies of exploring quantum many-body physics using deep neural networks (DNNs), despite of the tremendous success enjoyed by DNNs in many other areas in recent years. One main challenge of implementing DNN in VMC is the inefficiency of optimizing such networks with large number of parameters. We introduce an importance sampling gradient optimization (ISGO) algorithm, which significantly improves the computational speed of training DNN in VMC. We design an efficient convolutional DNN architecture to compute the ground state of a one-dimensional (1D) SU($N$) spin chain. Our numerical results of the ground-state energies with up to 16 layers of DNN show excellent agreement with the Bethe-Ansatz exact solution. Furthermore, we also calculate the loop correlation function using the wave function obtained. Our work demonstrates the feasibility and advantages of applying DNNs to numerical quantum many-body calculations.

arXiv comment8 pages, 7 figures

References in corpus (34)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Many-body quantum state tomography with neural networks
• Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms
• A one-dimensional liquid of fermions with tunable spin
• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Exact SO(5) Symmetry in spin 3/2 fermionic system
• Ultracold fermions and the SU(N) Hubbard model
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Symmetries and many-body excited states with neural-network quantum states
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods
• Approximating quantum many-body wave-functions using artificial neural networks
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Quantum Entanglement in Deep Learning Architectures
• Strongly interacting confined quantum systems in one dimension
• Direct probing of the Mott crossover in the SU($N$) Fermi-Hubbard model
• Quantum magnetism without lattices in strongly interacting one-dimensional spinor gases
• Constructing exact representations of quantum many-body systems with deep neural networks
• Machine learning technique to find quantum many-body ground states of bosons on a lattice
• Solving frustrated quantum many-particle models with convolutional neural networks
• Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
• Chiral Topological Phases from Artificial Neural Networks
• Strongly Interacting Quantum Gases in One-Dimensional Traps
• Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks
• DMRG simulations of SU(N) Heisenberg chains using standard Young tableaux: fundamental representation and comparison with finite-size Bethe ansatz
• Bose-Fermi Mapping and Multi-Branch Spin Chain Model for Strongly Interacting Quantum Gases in One-Dimension: Dynamics and Collective Excitations
• Hyperspatial optimisation of structures
• Variational Monte-Carlo investigation of SU($N$) Heisenberg chains
• Ground state phase diagram of the one-dimensional Bose-Hubbard model from restricted Boltzmann machines
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases

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