Work

Unified quantum framework for electrons and ions: The self-consistent harmonic approximation on a neural network curved manifold

Year: 2025

Type: article

Abstract: The numerical solution of the many-body problem, which involves interacting electrons and ions, is a key challenge in condensed matter physics, chemistry, and materials science. Traditional methods to solve the multicomponent 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 parameterized 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 that it can address both the ground- and excited-state properties of electronic systems, capture quantum tunneling and static electronic correlations, and thereby provide a unified quantum framework of electrons and atomic nuclei.

Source: Physical Review Research

DOI: 10.1103/7d6s-zz54

Authors: Lorenzo Monacelli, Antonio Siciliano, Nicola Marzari

Institutions: École Polytechnique Fédérale de Lausanne, Sapienza University of Rome

Language: English

Topic: Advanced Chemical Physics Studies

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625