A unified quantum framework for electrons and ions: The self-consistent harmonic approximation on a neural network curved manifold
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908606389026816 |
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| author | Monacelli, Lorenzo Siciliano, Antonio Marzari, Nicola |
| author_facet | Monacelli, Lorenzo Siciliano, Antonio Marzari, Nicola |
| contents | The numerical solution of the many-body problem of interacting electrons and ions is a key challenge in condensed matter physics, chemistry, and materials science. Traditional methods to solve the multi-component quantum Hamiltonian are usually specialized for one kind of particles -- electrons or ions -- and can suffer from a methodological gap when applied to the other ones.
This work extends the self-consistent harmonic approximation, a proven successful technique for simulating quantum ions at finite temperatures in anharmonic crystals, to electrons. The approach minimizes the total free energy by optimizing an ansatz density matrix, solving a fermionic self-consistent harmonic Hamiltonian on a curved manifold parametrized through a neural network. This approach preserves an analytical expression for entropy, enabling the direct computation of free energies and phase diagrams of materials. By benchmarking this technique across several prototypical cases -- a double-well potential, the hydrogen atom, and the H$_2$ dissociation -- we demonstrate it can address both the ground- and excited-state properties of electronic systems, capture quantum tunneling and static electronic correlations, thereby providing a unified quantum framework of electrons and atomic nuclei. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08882 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A unified quantum framework for electrons and ions: The self-consistent harmonic approximation on a neural network curved manifold Monacelli, Lorenzo Siciliano, Antonio Marzari, Nicola Materials Science Strongly Correlated Electrons The numerical solution of the many-body problem of interacting electrons and ions is a key challenge in condensed matter physics, chemistry, and materials science. Traditional methods to solve the multi-component quantum Hamiltonian are usually specialized for one kind of particles -- electrons or ions -- and can suffer from a methodological gap when applied to the other ones. This work extends the self-consistent harmonic approximation, a proven successful technique for simulating quantum ions at finite temperatures in anharmonic crystals, to electrons. The approach minimizes the total free energy by optimizing an ansatz density matrix, solving a fermionic self-consistent harmonic Hamiltonian on a curved manifold parametrized through a neural network. This approach preserves an analytical expression for entropy, enabling the direct computation of free energies and phase diagrams of materials. By benchmarking this technique across several prototypical cases -- a double-well potential, the hydrogen atom, and the H$_2$ dissociation -- we demonstrate it can address both the ground- and excited-state properties of electronic systems, capture quantum tunneling and static electronic correlations, thereby providing a unified quantum framework of electrons and atomic nuclei. |
| title | A unified quantum framework for electrons and ions: The self-consistent harmonic approximation on a neural network curved manifold |
| topic | Materials Science Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2410.08882 |