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Supplementing Recurrent Neural Network Wave Functions with Symmetry and Annealing to Improve Accuracy

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arxiv 2207.14314 v2 pith:JNIJWJND submitted 2022-07-28 cond-mat.dis-nn cond-mat.str-elcs.LGphysics.comp-ph

Mohamed Hibat-Allah , Roger G. Melko , Juan Carrasquilla This is my paper
classification cond-mat.dis-nncond-mat.str-elcs.LGphysics.comp-ph
keywords latticeneuralannealinggroundnetworkspowerfulrecurrentstate
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abstract

Recurrent neural networks (RNNs) are a class of neural networks that have emerged from the paradigm of artificial intelligence and has enabled lots of interesting advances in the field of natural language processing. Interestingly, these architectures were shown to be powerful ansatze to approximate the ground state of quantum systems. Here, we build over the results of [Phys. Rev. Research 2, 023358 (2020)] and construct a more powerful RNN wave function ansatz in two dimensions. We use symmetry and annealing to obtain accurate estimates of ground state energies of the two-dimensional (2D) Heisenberg model, on the square lattice and on the triangular lattice. We show that our method is superior to Density Matrix Renormalisation Group (DMRG) for system sizes larger than or equal to $14 \times 14$ on the triangular lattice.

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Cited by 7 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 of 10

    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. Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo

    cond-mat.str-el 2026-05 conditional novelty 7.0 of 10

    PSR-NQS makes recurrent neural quantum states scalable for variational Monte Carlo by using parallel scan recurrence, reaching accurate results on 52x52 two-dimensional lattices.

  3. New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures

    quant-ph 2026-04 unverdicted novelty 7.0 of 10

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

  4. Geometry-Induced Long-Range Correlations in Recurrent Neural Network Quantum States

    quant-ph 2026-04 conditional novelty 7.0 of 10

    Dilated RNN wave functions induce power-law correlations for the critical 1D transverse-field Ising model and the Cluster state, unlike the exponential decay of conventional RNN ansatze.

  5. New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures

    quant-ph 2026-04 conditional novelty 5.0 of 10

    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...

  6. New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures

    quant-ph 2026-04 conditional novelty 5.0 of 10

    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.

  7. Time-dependent Neural Galerkin Method for Quantum Dynamics

    quant-ph 2024-12 unverdicted novelty 5.0 of 10

    Presents a Neural Galerkin method that solves quantum dynamics globally via variational minimization of a Schrödinger loss, demonstrated on 1D/2D transverse-field Ising quenches showing non-thermalization in 2D.

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