Neural network wave functions and the sign problem

Abstract

Neural quantum states (NQS) are a promising approach to study many-body quantum physics. However, they face a major challenge when applied to lattice models: Convolutional networks struggle to converge to ground states with a nontrivial sign structure. We tackle this problem by proposing a neural network architecture with a simple, explicit, and interpretable phase ansatz, which can robustly represent such states and achieve state-of-the-art variational energies for both conventional and frustrated antiferromagnets. In the latter case, our approach uncovers low-energy states that exhibit the Marshall sign rule and are therefore inconsistent with the expected ground state. Such states are the likely cause of the obstruction for NQS-based variational Monte Carlo to access the true ground states of these systems. We discuss the implications of this observation and suggest potential strategies to overcome the problem.

arXiv comment12 pages, 7 figures. v3: authors' final version

References in corpus (35)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• The density-matrix renormalization group
• Machine learning and the physical sciences
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Area laws in quantum systems: mutual information and correlations
• Tensor networks for complex quantum systems
• Why does deep and cheap learning work so well?
• Generalized Lanczos Algorithm for Variational Quantum Monte Carlo
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg 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
• Fermionic neural-network states for ab-initio electronic structure
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Approximating quantum many-body wave-functions using artificial neural networks
• Quantum Entanglement in Deep Learning Architectures
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Neural Quantum States of frustrated magnets: generalization and sign structure
• NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
• Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
• Solving frustrated quantum many-particle models with convolutional neural networks
• Restricted Boltzmann Machines for Quantum States with Nonabelian or Anyonic Symmetries
• Ground-State Properties of Quantum Many-Body Systems: Entangled-Plaquette States and Variational Monte Carlo
• Neural Gutzwiller-projected variational wave functions
• Chiral Topological Phases from Artificial Neural Networks
• Shaping the learning landscape in neural networks around wide flat minima
• Geometry of learning neural quantum states
• On The Violation Of Marshall-Peierls Sign Rule In The Frustrated $J_1-J_2$ Heisenberg Antiferromagnet
• The learnability scaling of quantum states: restricted Boltzmann machines
• Area law and vacuum reordering in harmonic networks
• A machine learning approach to dynamical properties of quantum many-body systems
• Deep Learning-Enhanced Variational Monte Carlo Method for Quantum Many-Body Physics
• Machine Learning Quantum States -- Extensions to Fermion-Boson Coupled Systems and Excited-State Calculations
• Long-Range Entangled-Plaquette States for Critical and Frustrated Quantum Systems on a Lattice
• Marshall-Peierls sign rule for excited states of the frustrated J1-J2 Heisenberg antiferromagnet

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