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High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks
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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 ans\"atze. 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.
Forward citations
Cited by 4 Pith papers
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Two-dimensional Hyperbolic RNN Neural Quantum State
Lorentz 2DRNN introduces the first 2D hyperbolic NQS and outperforms Euclidean 2DRNN at the 2DTFIM critical point; 1D hyperbolic NQS also tested on reshaped 2D lattices.
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New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures
Hyperbolic RNN and GRU neural quantum states outperform Euclidean versions on Heisenberg J1J2 and J1J2J3 models with 100 spins.
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New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures
On 100-site Heisenberg J1-J2 and J1-J2-J3 chains, hyperbolic Poincaré/Lorentz RNN and GRU neural quantum states mostly beat Euclidean counterparts; Lorentz RNN wins four of eight settings despite about three times few...
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New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures
Hyperbolic recurrent networks, especially a Lorentz-model RNN, reach lower variational ground-state energies than Euclidean RNN/GRU wavefunctions on 100-spin Heisenberg chains, with up to three times fewer parameters.
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