Broken-Symmetry Ground States of the Heisenberg Model on the Pyrochlore Lattice

Astrakhantsev, Nikita; Westerhout, Tom; Tiwari, Apoorv; Choo, Kenny; Chen, Ao; Fischer, Mark H.; Carleo, Giuseppe; Neupert, Titus

doi:10.1103/physrevx.11.041021

Cited by 64 publications

(45 citation statements)

References 77 publications

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“…The general idea of the NQS method is to use the spin configuration σ as input for a neural network Ψ, interpreting the result Ψ(σ) as the (not normalized) wave function component, corresponding to the basis vector σ. To cope with the large system size and possible overfitting [53], we employ the convolutional neural network architecture (CNN) with real parameters and an elaborate alternating training technique [65]. This choice of architecture allows for better optimization and avoids certain instabilities [66].…”

Section: Neural Network Quantum Statesmentioning

confidence: 99%

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Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice

Astrakhantsev,

Westerhout,

Tiwari

et al. 2021

Preprint

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The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present. Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques. Specifically, we employ a RVB-like many-variable Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to 4 × 4 3 and 4 × 3 3 spins, respectively. We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit. Our main results are (1) the determination of the phase transition between the putative spin-liquid phase and the neighboring magnetically ordered phase and (2) a careful characterization of the ground state in terms of symmetry-breaking tendencies. We find clear indications of spontaneously broken inversion and rotational symmetry, calling the scenario of a featureless quantum spin-liquid into question. Our work showcases how many-variable variational techniques can be used to make progress in answering challenging questions about three-dimensional frustrated quantum magnets.

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Section: Neural Network Quantum Statesmentioning

confidence: 99%

“…In case of 3D frustrated magnets, the architecture alone turns out to be not enough to grasp the correct QSL ground state properties. To deal with frustrations, we introduce a novel algorithm of alternating learning [65]. It was initially shown in [74] that one can improve the final training result by performing training in two stages.…”

Section: ψ(σ) σmentioning

confidence: 99%

Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice

Astrakhantsev,

Westerhout,

Tiwari

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

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“…3) Since then, much effort has been made to improve the performance and extend the applicability of the method. Now, the neural-network method has been extended, e.g., to the simulations of spin systems with geometrical frustration, [4][5][6][7][8][9][10][11][12][13] itinerant boson systems, 14,15) fermion systems, 4,[16][17][18][19][20][21][22][23][24] fermion-boson coupled systems, 25) topologically nontrivial quantum states, [26][27][28][29][30][31][32] excited states, 10,22,25,[33][34][35] real-time evolution, 3,36,37) open quantum systems, [38][39][40][41] and finite-temperature properties. 42,43) Through various benchmarks using small system sizes that allow the exact diagonalization and special Hamiltonians for which the quantum Monte Carlo calculations can be perf...…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, recently, neuralnetwork wave functions have been applied to investigate the physics of frustrated quantum spin systems. 11,12) While there is growing numerical evidence that artificial neural networks are useful for accurately approximating quantum states, there is little understanding of what the machines have learned. This is due to the general problem that the machine learning process is a black box.…”

Section: Introductionmentioning

confidence: 99%

Investigating Network Parameters in Neural-Network Quantum States

Nomura

2022

Preprint

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Recently, quantum-state representation using artificial neural networks has started to be recognized as a powerful tool. However, due to the black-box nature of machine learning, it is difficult to analyze what machine learns or why it is powerful. Here, by applying one of the simplest neural networks, the restricted Boltzmann machine (RBM), to the ground-state representation of the one-dimensional (1D) transverse-field Ising (TFI) model, we make an attempt to directly analyze the optimized network parameters. In the RBM optimization, a zero-temperature quantum state is mapped onto a finite-temperature classical state of the extended Ising spins that constitute the RBM. We find that the quantum phase transition from the ordered phase to the disordered phase in the 1D TFI model by increasing the transversefield is clearly reflected in the behaviors of the optimized RBM parameters and hence in the finite-temperature phase diagram of the classical RBM Ising system. The present finding of a correspondence between the neural-network parameters and quantum phases suggests that a careful investigation of the neural-network parameters may provide a new route to extracting nontrivial physical insights from the neural-network wave functions.

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“…In this field, since the early research work, considerable attention was devoted to the problem of approximating ground-state wave functions of spin systems through artificial neural-networks. These representations, known as neural-network quantum states (NQS) 6 , can encode highly-entangled wave functions [7][8][9] , and are routinely used to study correlated quantum systems with discrete degrees of freedom [10][11][12][13][14][15][16][17] , often improving upon existing state-of-the-art results.…”

Section: Introductionmentioning

confidence: 99%

Neural-Network Quantum States for Periodic Systems in Continuous Space

Pescia,

Han,

Lovato

et al. 2021

Preprint

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We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of spatial periodicity. Our variational state is parameterized in terms of a permutationally-invariant part described by the Deep Sets neural-network architecture. The input coordinates to the Deep Sets are periodically transformed such that they are suitable to directly describe periodic bosonic systems. We show example applications to both one and two-dimensional interacting quantum gases with Gaussian interactions, as well as to 4 He confined in a one-dimensional geometry. For the one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.

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Broken-Symmetry Ground States of the Heisenberg Model on the Pyrochlore Lattice

Cited by 64 publications

References 77 publications

Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice

Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice

Investigating Network Parameters in Neural-Network Quantum States

Neural-Network Quantum States for Periodic Systems in Continuous Space

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