Comparing Sinc and Harmonic Oscillator Basis for Bound States of a Gaussian Interaction

Sharaf, Mamoon; McCarty, Ryan; Basili, Robert; Vary, James P.

doi:10.48550/arxiv.1912.07155

Cited by 1 publication

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“…2. It has to be emphasised that the ANN learns how to compensate for the original Gaussian confining function and reproduce the correct exponential falls off of the nuclear wave function, which is notoriously delicate to obtain within nuclear methods that rely on harmonic-oscillator basis expansions [52,53].…”

Section: Introduction -mentioning

confidence: 99%

Variational Monte Carlo calculations of $\mathbf{A\leq 4}$ nuclei with an artificial neural-network correlator ansatz

Adams,

Carleo,

Lovato

et al. 2020

Preprint

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The complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where non-perturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schrödinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field, which present exponentially-scaling algorithmic complexity. We compute the binding energies and point-nucleon densities of A ≤ 4 nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parametrizations based on two-and three-body Jastrow functions, and virtually-exact Green's function Monte Carlo results.

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Section: Introduction -mentioning

confidence: 99%