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arxiv 1807.09422 v2 pith:ZJ7DZHWL submitted 2018-07-25 cond-mat.str-el physics.comp-ph

Solving frustrated quantum many-particle models with convolutional neural networks

Xiao Liang , Wen-Yuan Liu , Pei-Ze Lin , Guang-Can Guo , Yong-Sheng Zhang , Lixin He This is my paper
classification cond-mat.str-el physics.comp-ph
keywords frustratedmachinemany-particlequantumlearningsolvesolvingbeen
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Two-dimensional Hyperbolic RNN Neural Quantum State

    quant-ph 2026-06 unverdicted novelty 7.0

    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.

  2. New non-Euclidean neural quantum states from additional types of hyperbolic recurrent neural networks

    quant-ph 2026-04 unverdicted novelty 7.0

    Hyperbolic RNN and GRU neural quantum states outperform Euclidean versions on Heisenberg J1J2 and J1J2J3 models with 100 spins.

  3. Universal Neural Propagator: Learning Time Evolution in Many-Body Quantum Systems

    quant-ph 2026-05 unverdicted novelty 6.0

    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.

  4. Graph-Theoretic Analysis of Phase Optimization Complexity in Variational Wave Functions for Heisenberg Antiferromagnets

    cond-mat.str-el 2026-02 accept novelty 6.0

    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.