arXiv subjects

Stefano Pittalis

Publications and source records attributed to Stefano Pittalis.

At least 19 recordsLinked to original sources

arXiv2026

A test drive for exchange-correlation functionals on noncollinear magnets: Mn$_3$Ir, Mn$_3$Ge, NiS$_2$, and YMnO$_3$

A first-principles description of noncollinear magnets is challenging, and the practical behavior of genuinely noncollinear exchange-correlation approximations is largely untested. Spin-current density-functional theory (SCDFT) admits noncollinear approximations constrained by local U(1)$\times$SU(2) gauge invariance, an exact condition unavailable in the more restrictive framework of spin-DFT (SDFT). Using the Vienna ab initio simulation package (VASP), we compare two recently developed noncollinear SCDFT functionals, NCMSCAN and LFNCBR89-NCCS, against locally collinear SDFT extensions of four common functionals (PZ, PW92, PBE, and SCAN) for several noncollinear $d$-electron systems. The key finding is that among all tested functionals, only the SCDFT functionals recover the spin texture of the experimental ground state of NiS$_2$, and they do so at a cost comparable to standard semi-local approximations. Yet the two SCDFT functionals differ in equilibrium volumes, band gaps, and on-site magnetic moments. Overall, this survey illustrates the usefulness of SCDFT in capturing noncollinear physics with the tested approximations.

cond-mat.mtrl-sci↗

arXiv2026

Thermal Fundamental Gap Predictions in DFT via Optimally Tuned Hybrids

Predicting electronic fundamental gaps at finite temperature has remained conceptually and practically challenging. We address this in three connected steps. First, we extend generalized Kohn--Sham hybrid density functional theory to thermal ensembles, deriving a Mermin generalized Kohn--Sham framework from a thermal one-particle auxiliary system and an exact density-functional remainder. Second, via an extension of Janak's theorem that holds rigorously in this framework, we recast Hirata's thermal-quasiparticle picture as a thermal orbital gap estimator and derive a closed low-temperature form, the error of which is controlled by the derivative discontinuity. Third, because optimal tuning eliminates this error, the auxiliary orbital gap matches the interacting gap at low temperature, upgrading optimal tuning from a ground-state strategy to the governing principle -- mandatory, not optional -- for accurate finite-temperature gap predictions obtained from gaps of orbital eigenvalues within a hybrid functional framework. We present applications that validate the theory and demonstrate its consequences.

physics.chem-ph↗

arXiv2026

Quantum-Information Measure of Electron Localization

Understanding electron localization in molecules and materials plays a central role in electronic structure theory, and will increase in importance with the rise of data-driven approaches. The electron localization function (ELF) is widely used to visualize electron organization in molecules and materials, and it remains a central ingredient in modern density-functional approximations. Yet its formulation retains highly empirical elements. Here we introduce a quantum-information measure of electron localization derived from the concurrence of a correlated two-spin mixed state. This construction yields a genuine two-point localization indicator grounded in quantum-information theory, avoiding the heuristic normalization and chosen nonlinear remapping of the ELF. We show that atomic shells, covalent and ionic bonds, lone pairs, molecular dissociation, and charge-transfer processes are captured. The method is straightforward to evaluate numerically.

cond-mat.mtrl-sci↗

arXiv2026

Semi-Local Exchange-Correlation Approximations in Density Functional Theory

Density functional theory has become the workhorse of modern electronic structure calculations, with wide-ranging applications in chemistry, physics, materials science, biochemistry, etc. At its heart lies the exchange-correlation functional, a quantity which exactly encapsulates the many-body effects stemming from the quantum mechanical interactions between the electrons. Yet, the exact functional is unknown, and computationally tractable approximations are therefore necessary for practical applications. Over the past six decades, hundreds of density functional approximations have been proposed with varying accuracy and computational efficiency. This review surveys the theoretical foundations of semi-local functionals, including local density approximations, generalized gradient approximations, and meta-generalized gradient approximations. We provide a comprehensive, consistently organized discussion that consolidates both historical developments and recent advances in this field. Beginning with the essentials of Kohn-Sham density functional theory, we present the construction principles of semi-local exchange-correlation functionals. Special attention is given to the physical motivations underlying functional development, the mathematical properties that guide their construction, and the practical considerations that determine their applicability across different chemical and physical systems. This work is intended to serve as both an introduction for newcomers to the field and a comprehensive reference for practitioners. By consolidating the extensive literature on semi-local functionals and providing a unified framework for their construction and application, we aim to facilitate further developments in density functional approximations and their use in tackling the diverse challenges of modern computational chemistry and condensed matter physics.

physics.chem-ph↗

arXiv2025

Physical spin torques from exactly constrained exchange-correlation torques

The problem of capturing physical spin torques in non-collinear magnetic systems has dominated the scene of spin-density functional theory (SDFT) in the last two decades. Progress has been hindered by the fact that the spin torque is directly connected to the divergence of the spin current, a quantity that is {\em extraneous} to SDFT -- thus leading to {\em spurious} exchange-correlation (xc) torques in the spin dynamics. Moreover, SDFT cannot rigorously include vector potentials and spin-orbit couplings. Here, we propose a solution that exploits the U(1)$\times$SU(2)-invariance of the xc energy of SpinCurrent-DFT (SCDFT) -- an exact constraint that is not accessible to SDFT. Non-vanishing xc torques obtained on non-collinear solutions are constrained by the aforementioned exact internal symmetry and do not enter the propagation of the spin magnetization -- i.e., the spin dynamics involve {\em only} the physical currents and physical spin-torques.

cond-mat.mtrl-sci↗

arXiv2025

Spins extracted from fermionic states and their entanglement properties

We investigate the spin states obtained by extracting $n$ electrons from closed-shell fermionic states. A partition of the system is defined through the introduction of the extraction modes. We derive the expression of the $n$-body reduced density matrices, which represent the extracted spin states. We show that these states exhibit different forms of spin entanglement, whose detection is discussed in terms of the spin squeezing inequalities.

quant-ph↗

arXiv2025

"Ensemblization" of density functional theory

Density functional theory (DFT) has transformed our ability to investigate and understand electronic ground states. In its original formulation, however, DFT is not suited to addressing (e.g.) degenerate ground states, mixed states with different particle numbers, or excited states. All these issues can be handled, in principle exactly, via ensemble DFT (EDFT). This Perspective provides a detailed introduction to and analysis of EDFT, in an in-principle exact framework that is constructed to avoid uncontrolled errors and inconsistencies that may be associated with {\it ad hoc} extensions of conventional DFT. In particular, it focuses on the "ensemblization" of both exact and approximate density functionals, a term we coin to describe a rigorous approach that lends itself to the construction of novel approximations consistent with the general ensemble framework, yet applicable to practical problems where traditional DFT tends to fail or does not apply at all. Specifically, symmetry considerations and ensemble properties are shown to enable each other in shaping a practical DFT-based methodology that extends beyond the ground state and, in doing so, highlights the need to look outside the standard ground state Kohn-Sham treatment.

physics.chem-ph↗

arXiv2024

Genuine multipartite entanglement from many-electron systems

We demonstrate that, contrary to common wisdom, genuine multipartite entanglement (GME) can be abundantly generated from simple non-correlated many-electron states. We show that the extracted GME can be maximized via spin-independent transformations derived from the quantum Fourier transform. We further demonstrate the possibility of maximizing the GME through localized orbitals in a variety of realistic systems and correlated states. Towards the exploitation of potentially useful entanglement, we rationalize system-specific and universal features of the extracted GME.

quant-ph↗

arXiv2024

Meta-Generalized-Gradient Approximation made Magnetic

The Jacob's ladder of density functional theory (DFT) proposes the compelling view that by extending the form of successful approximations -- being guided by exact conditions and selected (least empirical) norms -- upper rungs will do better than the lower, thus allowing to balance accuracy and computational effort. Meta-generalized-gradient-approximations (MGGAs) belong to the last rung of the semi-local approximations before hybridization with non-local wave function theories. Among the MGGAs, the Strongly Constrained and Appropriately Normed Approximation (SCAN) greatly improves upon GGAs from the lower rung. But the over magnetized solutions of SCAN make GGAs more reliable for magnetism. Here, we provide a solution that satisfies the most pressing {\em desiderata} for density functional approximations for ferromagnetic, antiferromagnetic and non-collinear states. The approach is available in an implementation in the \textsc{Crystal} electronic structure package.

cond-mat.mtrl-sci↗

arXiv2024

State-specific density functionals for excited states from ensembles

We present a first principles strategy for developing state-specific density functional approximations for excited states. We first clarify why approaches based on conventional ground state approximations miss density-driven correlations, by considering excited state physics through the lens of ensemble density functional theory. To solve this issue we gain insights on density driven correlations by exploiting the recently understood low-density limit of electrons in excited states. The theory developments are then combined to produce a proof-of-concept excited state approximation that resolves urgent paradigmatic failures (double excitations, charge transfer excitations, piecewise linearity) of existing state-of-art density-functional approaches, directly from differences of self-consistent field calculations; i.e., $\Delta$SCF. In light of its observed impressive performance, we conclude that the approach represents a major step toward unified and accurate modelling of neutral and charged excitations.

physics.chem-ph↗

arXiv2024

Electron localization function for non-collinear spins

Understanding of bonding is key to modelling materials and predicting properties thereof. A widely adopted indicator of bonds and atomic shells is the electron localization function (ELF). The building blocks of the ELF are also used in the construction of modern density functional approximations. Here we demonstrate that the ELF breaks down when applied beyond regular non-relativistic quantum states. We show that for tackling general non-collinear open-shell solutions, it is essential to address both the U(1) gauge invariance -- i.e., invariance under a multiplication by a position dependent phase factor -- and SU(2) gauge invariance -- i.e. invariance under local spin rotations -- {\em conjointly}. Remarkably, we find that the extended ELF also improves the description of paradigmatic collinear states.

cond-mat.mtrl-sci↗

arXiv2024

Spin-currents via the gauge-principle for meta-generalized-gradient exchange-correlation functionals

The prominence of density functional theory (DFT) in the field of electronic structure computation stems from its ability to usefully balance accuracy and computational effort. At the base of this ability is a functional of the electron density: the exchange-correlation energy. This functional satisfies known exact conditions that guide the derivation of approximations. The strongly-constrained-appropriately-normed (SCAN) approximation stands out as a successful, modern, example. In this work, we demonstrate how the SU(2) gauge-invariance of the exchange-correlation functional in spin current density functional theory allows us to add an explicit dependence on spin currents in the SCAN functional (here called JSCAN) -- and similar meta-generalized-gradient functional approximations -- solely invoking first principles. In passing, a spin-current dependent generalization of the electron localization function (here called JELF) is also derived. The extended forms are implemented in a developer's version of the \textsc{Crystal23} program. Applications on molecules and materials confirm the practical relevance of the extensions.

cond-mat.mtrl-sci↗

arXiv2023

Generalized Kohn-Sham Approach for the Electronic Band Structure of Spin-Orbit Coupled Materials

Spin-current density functional theory (SCDFT) is a formally exact framework designed to handle the treatment of interacting many-electron systems including spin-orbit coupling at the level of the Pauli equation. In practice, robust and accurate calculations of the electronic structure of these systems call for functional approximations that depend not only on the densities, but also on spin-orbitals. Here we show that the call can be answered by resorting to an extension of the Kohn-Sham formalism, which admits the use of non-local effective potentials, yet it is firmly rooted in SCDFT. The power of the extended formalism is demonstrated by calculating the spin-orbit-induced band-splittings of inversion-asymmetric MoSe$_2$ monolayer and inversion-symmetric bulk $\alpha$-MoTe$_2$. We show that quantitative agreement with experimental data is obtainable via global hybrid approximations by setting the fraction of Fock exchange at the same level which yields accurate values of the band gap. Key to these results is the ability of the method to self-consistently account for the spin currents induced by the spin-orbit interaction. The widely used method of refining spin-density functional theory by a second-variational treatment of spin-orbit coupling is unable to match our SCDFT results.

cond-mat.mtrl-sci↗

arXiv2023

Local density approximation for excited states

The ground state of an homogeneous electron gas is a paradigmatic state that has been used to model and predict the electronic structure of matter at equilibrium for nearly a century. For half a century, it has been successfully used to predict ground states of quantum systems via the local density approximation (LDA) of density functional theory (DFT); and systematic improvements in the form of generalized gradient approximations and evolution thereon. Here, we introduce the LDA for \emph{excited} states by considering a particular class of non-thermal ensemble states of the homogeneous electron gas. These states find sound foundation and application in ensemble-DFT -- a generalization of DFT that can deal with ground and excited states on equal footing. The ensemble-LDA is shown to successfully predict difficult low-lying excitations in atoms and molecules for which approximations based on local spin density approximation (LSDA) and time-dependent-LDA fail.

physics.chem-ph↗

arXiv2022

Field-driven attosecond photoinjection dynamics in semiconductors

The route towards manipulation of the optoelectronic properties of matter beyond the current limits of electronics starts from a comprehensive study of the ultrafast dynamics triggered by interaction with light. Among them, a fundamental role is played by charge photoinjection, a complex process that stems from the interplay of many different physical phenomena, which cannot be easily disentangled. Single- and multi-photon absorption, diabatic tunnelling, intra-band motion, and field-driven band dressing, all concur in determining the overall excited electron population, dictating the electro-optical properties of a material. Here we investigate ultrafast photoinjection in a prototypical semiconductor (monocrystalline germanium) by using attosecond transient reflection spectroscopy. The precise pump-field characterization ensured by a simultaneous attosecond streaking experiment, in tandem with a comprehensive theoretical approach, allowed us to disentangle the different physical phenomena unfolding at different positions in the reciprocal space and at different timing within the envelope of the pump pulse. Moreover, we found that intra-band phenomena hinder charge injection, in contrast to what was previously observed for resonant, direct band-gap semiconductors. Therefore, besides other known parameters as the central wavelength and peak intensity, our results indicate that the pulse temporal envelope and the local band structure probed by intra-band effects are of key importance to achieve an optimal control over the ultrafast carrier injection process and tailor the complex optical and electronic properties of a semiconductor on the few- to sub-femtosecond time scale.

physics.optics↗

arXiv2022

Electronic excited states in extreme limits via ensemble density functionals

Density functional theory (DFT) has greatly expanded our ability to affordably compute and understand electronic ground states, by replacing intractable {\em ab initio} calculations by models based on paradigmatic physics from high- and low-density limits. But, a comparable treatment of excited states lags behind. Here, we solve this outstanding problem by employing a generalization of density functional theory to ensemble states (EDFT). We thus address important paradigmatic cases of all electronic systems in strongly (low-density) and weakly (high-density) correlated regimes. We show that the high-density limit connects to recent, exactly-solvable EDFT results. The low-density limit reveals an unnoticed and most unexpected result -- density functionals for strictly correlated {\em ground} states can be reused {\em directly} for excited states. Non-trivial dependence on excitation structure only shows up at third leading order. Overall, our results provide foundations for effective models of excited states that interpolate between exact low- and high-density limits, which we illustrate on the cases of singlet-singlet excitations in H$_2$ and a ring of quantum wells.

physics.chem-ph↗

arXiv2022

Excitations of Quantum Many-Body Systems via Purified Ensembles: A Unitary-Coupled-Cluster-based Approach

State-average calculations based on mixture of states are increasingly being exploited across chemistry and physics as versatile procedures for addressing excitations of quantum many-body systems. If not too many states should need to be addressed, calculations performed on individual states is also a common option. Here we show how the two approaches can be merged into one method, dealing with a generalized yet single pure state. Implications in electronic structure calculations are discussed and for quantum computations are pointed out.

quant-ph↗

arXiv2021

Ensemble reduced density matrix functional theory for excited states and hierarchical generalization of Pauli's exclusion principle

We propose and work out a reduced density matrix functional theory (RDMFT) for calculating energies of eigenstates of interacting many-electron systems beyond the ground state. Various obstacles which historically have doomed such an approach to be unfeasible are overcome. First, we resort to a generalization of the Ritz variational principle to ensemble states with fixed weights. This in combination with the constrained search formalism allows us to establish a universal functional of the one-particle reduced density matrix. Second, we employ tools from convex analysis to circumvent the too involved N-representability constraints. Remarkably, this identifies Valone's pioneering work on RDMFT as a special case of convex relaxation and reveals that crucial information about the excitation structure is contained in the functional's domain. Third, to determine the crucial latter object, a methodology is developed which eventually leads to a generalized exclusion principle. The corresponding linear constraints are calculated for systems of arbitrary size.

quant-ph↗