arXiv subjects

Miguel Escobar Azor

Publications and source records attributed to Miguel Escobar Azor.

6 recordsLinked to original sources

arXiv2025

Spin-Dependent Nonorthogonal Generalized Wannier Functions and their Integration with PAW and Hubbard Corrections in Linear-Scaling DFT

We present a spin-dependent extension of the non-orthogonal generalized Wannier function (NGWF) formalism within the framework of linear-scaling density functional theory (LS-DFT) as implemented in the ONETEP code. In traditional LS-DFT representations, both spin channels are constrained to share a common variational basis, which limits the accuracy for systems that are spin-polarized or exhibit magnetic order. Our approach allows NGWFs to vary independently for each spin channel, enabling a more accurate representation of spin-polarization in the electronic density. We demonstrate the efficacy of this method through a series of test cases, including localized magnetic defects in two-dimensional hBN, transition metal complexes, two-dimensional van der Waals magnetic materials, and both bulk and nanocluster ferromagnetic Co. In each scenario, the incorporation of spin-dependent NGWFs results in enhanced accuracy for total energy calculations, improved localization of spin density, and accurate predictions of magnetic ground states. This improvement is particularly notable when combined with DFT+U and DFT+U+J corrections. In this work, we take the opportunity to describe the combination of DFT+U+J and the projector-augmented wave (PAW) formalism within the LS-DFT framework, including how PAW participates in the ionic Pulay force, and in the minimum-tracking linear response approach for computing parameters in situ. Our findings demonstrate that spin-dependent NGWFs are a crucial and computationally efficient advancement in the linear-scaling DFT simulation of spin-polarized materials.

cond-mat.mtrl-sci↗

arXiv2024

The Emergence of the Hexagonal Lattice in Two-Dimensional Wigner Fragments

At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density profiles of fragments of Wigner crystals from first principles. To simulate Wigner fragments we use Clifford periodic boundary conditions and a renormalized distance in the Coulomb potential. Moreover, we show that high-spin restricted open-shell Hartree-Fock theory becomes exact in the low-density limit. We are thus able to accurately capture the localisation in two-dimensional Wigner fragments with many electrons. No assumptions about the positions where the electrons will localise are made. The density profiles we obtain emerge naturally when we minimise the total energy of the system. We clearly observe the emergence of the hexagonal crystal structure which has been predicted to be ground-state structure of the two-dimensional Wigner crystal.

quant-ph↗

arXiv2023

Solution to the Thomson problem for Clifford tori with an application to Wigner crystals

In its original version, the Thomson problem consists of the search for the minimum-energy configuration of a set of point-like electrons that are confined to the surface of a two-dimensional sphere (${\cal S}^2$) that repel each other according to Coulomb's law, in which the distance is the Euclidean distance in the embedding space of the sphere, {\em i.e.}, $\mathbb{R}^3$. In this work, we consider the analogous problem where the electrons are confined to an $n$-dimensional flat Clifford torus ${\cal T}^n$ with $n = 1, 2, 3$. Since the torus ${\cal T}^n$ can be embedded in the complex manifold $\mathbb{C}^n$, we define the distance in the Coulomb law as the Euclidean distance in $\mathbb{C}^n$, in analogy to what is done for the Thomson problem on the sphere. The Thomson problem on a Clifford torus is of interest because super-cells with the topology of Clifford torus can be used to describe periodic systems such as Wigner crystals. In this work we numerically solve the Thomson problem on a square Clifford torus. To illustrate the usefulness of our approach we apply it to Wigner crystals. We demonstrate that the equilibrium configurations we obtain for a large numbers of electrons are consistent with the predicted structures of Wigner crystals. Finally, in the one-dimensional case we analytically obtain the energy spectrum and the phonon dispersion law.

cond-mat.other↗

arXiv2022

The Wigner localization of interacting electrons in a one-dimensional harmonic potential

approaches. We demonstrate that the Wigner regime can be reached using small values of the confinement parameter. To obtain physical insight in our results we analyze them with a semi-analytical model for two electrons. Thanks to electronic-structure properties such as the one-body density and the particle-hole entropy, we are able to define a path that connects the Wigner regime to the Fermi-gas regime by varying the confinement parameter. In particular, we show that the particle-hole entropy as a function of the confinement parameter smoothly connects the two regimes. Moreover, it exhibits a maximum that could be interpreted as the transition point between the localized and delocalized regimes.

cond-mat.str-el↗

arXiv2021

Wigner localization in two and three dimensions: an \emph{ab initio} approach

In this work we investigate the Wigner localization of two interacting electrons at very low density in two and three dimensions using the exact diagonalization of the many-body Hamiltonian. We use our recently developed method based on Clifford periodic boundary conditions with a renormalized distance in the Coulomb potential. To accurately represent the electronic wave function we use a regular distribution in space of gaussian-type orbitals and we take advantage of the translational symmetry of the system to efficiently calculate the electronic wave function. We are thus able to accurately describe the wave function up to very low density. We validate our approach by comparing our results to a semi-classical model that becomes exact in the low-density limit. With our approach we are able to observe the Wigner localization without ambiguity.

cond-mat.str-el↗

arXiv2019

A Wigner molecule at extremely low densities: a numerically exact study

In this work we investigate Wigner localization at very low densities by means of the exact diagonalization of the Hamiltonian. This yields numerically exact results. In particular, we study a quasi-one-dimensional system of two electrons that are confined to a ring by three-dimensional gaussians placed along the ring perimeter. To characterize the Wigner localization we study several appropriate observables, namely the two-body reduced density matrix, the localization tensor and the particle-hole entropy. We show that the localization tensor is the most promising quantity to study Wigner localization since it accurately captures the transition from the delocalized to the localized state and it can be applied to systems of all sizes.

cond-mat.str-el↗