Machine learning one-dimensional spinless trapped fermionic systems with neural-network quantum states

We compute the ground-state properties of fully polarized, trapped, one-dimensional fermionic systems interacting through a gaussian potential. We use an antisymmetric artificial neural network, or neural quantum state, as an ansatz for the wavefunction and use machine learning techniques to variati...

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Bibliographic Details
Published in:arXiv.org 2024-02
Main Authors: Keeble, J W T, Drissi, M, Rojo-Francàs, A, Juliá-Díaz, B, Rios, A
Format: Article
Language:English
Subjects:
Artificial neural networks
Computing time
Hartree approximation
Machine learning
Wave functions
Online Access:Get full text
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Summary:We compute the ground-state properties of fully polarized, trapped, one-dimensional fermionic systems interacting through a gaussian potential. We use an antisymmetric artificial neural network, or neural quantum state, as an ansatz for the wavefunction and use machine learning techniques to variationally minimize the energy of systems from 2 to 6 particles. We provide extensive benchmarks with other many-body methods, including exact diagonalisation and the Hartree-Fock approximation. The neural quantum state provides the best energies across a wide range of interaction strengths. We find very different ground states depending on the sign of the interaction. In the non-perturbative repulsive regime, the system asymptotically reaches crystalline order. In contrast, the strongly attractive regime shows signs of bosonization. The neural quantum state continuously learns these different phases with an almost constant number of parameters and a very modest increase in computational time with the number of particles.
ISSN:2331-8422
DOI:10.48550/arxiv.2304.04725