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.
Solving frustrated quantum many-particle models with convolutional neural networks
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abstract
Recently, there has been significant progress in solving quantum many-particle problem via machine learning based on the restricted Boltzmann machine. However, it is still highly challenging to solve frustrated models via machine learning, which has not been demonstrated so far. In this work, we design a brand new convolutional neural network (CNN) to solve such quantum many-particle problems. We demonstrate, for the first time, of solving the highly frustrated spin-1/2 J$_1$-J$_2$ antiferromagnetic Heisenberg model on square lattices via CNN. The energy per site achieved by the CNN is even better than previous string-bond-state calculations. Our work therefore opens up a new routine to solve challenging frustrated quantum many-particle problems using machine learning.
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Ground-state phase reconstruction for Heisenberg antiferromagnets with fixed amplitudes is equivalent to weighted Max-Cut on the Hilbert-space graph, establishing worst-case NP-hardness.
The Universal Neural Propagator is a single neural model trained self-supervised to predict time evolution in driven quantum many-body systems across arbitrary protocols and initial states.
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.
citing papers explorer
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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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Graph-Theoretic Analysis of Phase Optimization Complexity in Variational Wave Functions for Heisenberg Antiferromagnets
Ground-state phase reconstruction for Heisenberg antiferromagnets with fixed amplitudes is equivalent to weighted Max-Cut on the Hilbert-space graph, establishing worst-case NP-hardness.
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Universal Neural Propagator: Learning Time Evolution in Many-Body Quantum Systems
The Universal Neural Propagator is a single neural model trained self-supervised to predict time evolution in driven quantum many-body systems across arbitrary protocols and initial states.
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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.