arXiv subjects

Antonio Siciliano

Publications and source records attributed to Antonio Siciliano.

4 recordsLinked to original sources

arXiv2025

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

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.

cond-mat.mtrl-sci↗

arXiv2024

Beyond Gaussian fluctuations of quantum anharmonic nuclei. The case of rotational degrees of freedom

The atomic motion in molecular crystals, such as high-pressure hydrogen or hybrid organic-inorganic perovskites, is very complex due to quantum anharmonic effects. In addition, these materials accommodate rotational degrees of freedom. All the approximate methods that describe the nuclei thermodynamics using Cartesian coordinates lead to an unphysical hybridization of roto-librations with other high-energy modes. Hence, they do not accurately account for the free energy contributions of these degrees of freedom. So, a reliable description of a molecular crystal's phase diagram is only possible with Path Integral Molecular Dynamics (PIMD) at a high computational cost. This work shows how to include roto-librational modes in the Self-Consistent Harmonic Approximation (SCHA) framework. SCHA approximates the nuclei Cartesian fluctuations to be Gaussian, thus neglecting curvilinear motion. Keeping its low computational cost, we employ the generalization of SCHA, called nonlinear SCHA (NLSCHA). Our method relies on a Gaussian \textit{ansatz} for the nuclei density matrix on a curved manifold, allowing us to map roto-librations into harmonic modes defined on a surface. By optimizing the surface's curvature variationally, we minimize the free energy, allowing the spontaneous activation of these degrees of freedom without external parameters. Notably, in the limit of vanishing curvature, we recover the standard SCHA.

cond-mat.mtrl-sci↗

arXiv2024

Beyond Gaussian fluctuations of quantum anharmonic nuclei

The Self-Consistent Harmonic Approximation (SCHA) describes atoms in solids, including quantum fluctuations and anharmonic effects, in a non-perturbative way. It computes ionic free energy variationally, constraining the atomic quantum-thermal fluctuations to be Gaussian. Consequently, the entropy is analytical; there is no need for thermodynamic integration or heavy diagonalization to include finite temperature effects. In addition, as the probability distribution is fixed, SCHA solves all the equations with Monte Carlo integration without employing Metropolis sampling of the quantum phase space. Unfortunately, the Gaussian approximation breaks down for rotational modes and tunneling effects. We show how to describe these non-Gaussian fluctuations using the quantum variational principle at finite temperatures, keeping the main advantage of SCHA: direct access to free energy. Our method, nonlinear SCHA (NLSCHA), employs an invertible nonlinear transformation to map Cartesian coordinates into an auxiliary manifold parametrized by a finite set of variables. So, we adopt a Gaussian \textit{ansatz} for the density matrix in this new coordinate system. The nonlinearity of the mapping ensures that NLSCHA enlarges the SCHA variational subspace, and its invertibility conserves the information encoded in the density matrix. We evaluate the entropy in the auxiliary space, where it has a simple analytical form. As in the SCHA, the variational principle allows for optimizing free parameters to minimize free energy. Finally, we show that, for the first time, NLSCHA gives direct access to the entropy of a crystal with non-Gaussian degrees of freedom.

cond-mat.mtrl-sci↗

arXiv2023

Wigner Gaussian dynamics: simulating the anharmonic and quantum ionic motion

The atomic motion controls important features of materials, such as thermal transport, phase transitions, and vibrational spectra. However, the simulation of ionic dynamics is exceptionally challenging when quantum fluctuations are relevant (e.g., at low temperatures or with light atoms) and the energy landscape is anharmonic. In this work, we formulate the Time-Dependent Self-Consistent Harmonic Approximation (TDSCHA) in the Wigner framework, paving the way for the efficient computation of the nuclear motion in systems with sizable quantum and thermal anharmonic fluctuations. Besides the improved numerical efficiency, the Wigner formalism unveils the classical limit of TDSCHA and provides a link with the many-body perturbation theory of Feynman diagrams. We further extend the method to account for the non-linear couplings between phonons and photons, responsible, e.g., for a nonvanishing Raman signal in high-symmetry Raman inactive crystals, firstly discussed by Rasetti and Fermi. We benchmark the method in phase III of high-pressure hydrogen ab initio. The nonlinear photon-phonon coupling reshapes the IR spectra and explains the high-frequency shoulder of the H2 vibron observed in experiments. The Wigner TDSCHA is computationally cheap and derived from first principles: it is unbiased by assumptions on the phonon-phonon and phonon-photon scattering and does not depend on empirical parameters. Therefore, the method can be adopted in unsupervised high-throughput calculations.

cond-mat.mtrl-sci↗