High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks

Abstract

We show that neural quantum states based on very deep (4--16-layered) neural networks can outperform state-of-the-art variational approaches on highly frustrated quantum magnets, including quantum-spin-liquid candidates. We focus on group convolutional neural networks (GCNNs) that allow us to impose space-group symmetries on our ansätze. We achieve state-of-the-art ground-state energies for the $J_1-J_2$ Heisenberg models on the square and triangular lattices, in both ordered and spin-liquid phases, and discuss ways to access low-lying excited states in nontrivial symmetry sectors. We also compute spin and dimer correlation functions for the quantum paramagnetic phase on the triangular lattice, which do not indicate either conventional or valence-bond ordering.

arXiv comment12 pages, 8 figures

References in corpus (45)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Quantum Spin Liquids
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Quantum Natural Gradient
• Exact spectra, spin susceptibilities and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Spin liquid nature in the Heisenberg $J_1$-$J_2$ triangular antiferromagnet
• Green Function Monte Carlo with Stochastic Reconfiguration
• Recurrent Neural Network Wave Functions
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study
• Dirac Spin Liquid on the Spin-1/2 Triangular Heisenberg Antiferromagnet
• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Neural Quantum States of frustrated magnets: generalization and sign structure
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Chiral Spin Liquid and Quantum Criticality in Extended $S=1/2$ Heisenberg Models on the Triangular Lattice
• Unifying Description of Competing Orders in Two Dimensional Quantum Magnets
• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
• Restricted Boltzmann Machines for Quantum States with Nonabelian or Anyonic Symmetries
• mVMC - Open-source software for many-variable variational Monte Carlo method
• Ground-state phase diagram of the quantum $J_1-J_2$ model on the square lattice
• Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model
• Gapless spin liquid and valence-bond solid in the $J_1-J_2$ Heisenberg model on the square lattice: insights from singlet and triplet excitations
• Neural network wave functions and the sign problem
• Dynamical structure factor of the triangular antiferromagnet: the Schwinger boson theory beyond the mean field approach
• From spinon band topology to the symmetry quantum numbers of monopoles in Dirac spin liquids
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
• The emergence of gapless quantum spin liquid from deconfined quantum critical point
• Avoided quasiparticle decay and enhanced excitation continuum in the spin-1/2 near-Heisenberg triangular antiferromagnet Ba3CoSb2O9
• Optimizing Design Choices for Neural Quantum States
• Pinch-points to half-moons and up in the stars: the kagome skymap
• Many-Body Quantum States with Exact Conservation of Non-Abelian and Lattice Symmetries through Variational Monte Carlo
• Anisotropic deconfined criticality in Dirac spin liquids

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• Group Convolutional Neural Network for the Low-Energy Spectrum in the Quantum Dimer Model
• Hybrid between biologically and quantum-inspired many-body states
• Comparing Symmetrized Determinant Neural Quantum States for the Hubbard Model
• Optimizing the dynamical preparation of quantum spin lakes on the ruby lattice
• Field-induced states and thermodynamics of the frustrated Heisenberg antiferromagnet on a square lattice