arXiv subjects

Celestino Angeli

Publications and source records attributed to Celestino Angeli.

10 recordsLinked to original sources

arXiv2026

Symmetry-driven correlation patterns in one-dimensional periodic fermionic systems: closed-form expressions and exact selection rules for correlation functions, entanglement entropies and mutual information

We present an analytical study of the spatial structure of correlations in periodic fermionic systems at the single Slater determinant level, focusing on the cyclic case. Exploiting cyclic symmetry, the transformation from localized orbitals to molecular orbitals is simultaneously a discrete Fourier transform, a Vandermonde matrix on the roots of unity, a complex Hadamard matrix, and the character table of the cyclic group $C_m$. Within this framework, the spatial structure of correlations is fully determined by the occupied irreducible representations (Fourier modes), independently of the specific Hamiltonian generating them. In particular, the fermionic two-point correlator is expressed as a truncated Fourier sum over the occupied orbitals, leading to exact analytical expressions for symmetric occupation patterns of Fourier modes ($\ell$ and $-\ell$ pairs), corresponding in quantum chemistry to aromatic fillings, i.e. fillings satisfying Hückel's $4n + 2$ rule. For the half filling case, we derive exact spatial selection rules. In particular, the two-point correlator vanishes identically for all even distances along the ring. This property propagates to reduced density matrices and implies a complete absence of mutual information between the corresponding orbitals. These results reveal that, despite the global delocalization of molecular orbitals, the correlation structure in cyclic systems is highly non-uniform and governed by symmetry-induced interference. Although formulated in terms of cyclic lattice systems, the present results extend straightforwardly to one-dimensional fermionic chains with periodic conditions, reflecting the underlying translational symmetry of the problem. The framework therefore provides a Hamiltonian-independent and universal reference for understanding correlation patterns in one-dimensional periodic fermionic systems.

quant-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↗

arXiv2025

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

Quantum Information reveals that orbital-wise correlation is essentially classical in Natural Orbitals

The intersection of Quantum Chemistry and Quantum Computing has led to significant advancements in understanding the potential of using quantum devices for the efficient calculation of molecular energies. Simultaneously, this intersection is enhancing the comprehension of quantum chemical properties through the use of quantum computing and quantum information tools. This paper tackles a key question in this relationship: Is the nature of the orbital-wise electron correlations in wavefunctions of realistic prototypical cases classical or quantum? We delve into this inquiry with a comprehensive examination of molecular wavefunctions using Shannon and von Neumann entropies, alongside classical and quantum information theory. Our analysis reveals a notable distinction between classical and quantum mutual information in molecular systems when analyzed with Hartree-Fock canonical orbitals. However, this difference decreases dramatically, by approximately 100-fold, when Natural Orbitals are used as reference. This finding suggests that wavefunction correlations, when viewed through the appropriate orbital basis, are predominantly classical. This insight indicates that computational tasks in quantum chemistry could be significantly simplified by employing Natural Orbitals. Consequently, our study underscores the importance of using Natural Orbitals to accurately assess molecular wavefunction correlations and to avoid their overestimation. In summary, our results suggest a promising path for computational simplification in quantum chemistry, advocating for the wider adoption of Natural Orbitals and raising questions about the actual computational complexity of the multi-body problem in quantum chemistry.

quant-ph↗

arXiv2023

Quantum Information Driven Ansatz (QIDA): shallow-depth empirical quantum circuits from Quantum Chemistry

Hardware-efficient empirical variational ansätze for Variational Quantum Eigensolver simulations of Quantum Chemistry suffer from the lack of a direct connection to classical Quantum Chemistry methods. In the present work, we propose a method to fill this gap by introducing a new approach for constructing variational quantum circuits, leveraging quantum mutual information associated with classical Quantum Chemistry states to design simple yet effective heuristic ansätze with a topology that reflects the correlations of the molecular system. As first step, Quantum Chemistry calculations, such as Møller-Plesset (MP2) perturbation theory, firstly provide an approximate Natural Orbitals basis, which has been recently shown to be the best candidate one-electron basis for developing compact empirical wavefunctions (Ratini, et al 2023). Secondly, throughout the evaluation of quantum mutual information matrices, they provide information about the main correlations between qubits of the quantum circuit, enabling the development of a direct design of entangling blocks for the circuit. The resulting ansatz is then utilized with a Variational Quantum Eigensolver (VQE) to obtain a short depth variational groundstate of the electronic Hamiltonian. To validate our approach, we perform a comprehensive statistical analysis by simulations over various molecular systems ($H_2, LiH, H_2O$) and apply it to the more complex $NH_3$ molecule. The reported results demonstrate that the proposed methodology gives rise to highly effective ansätze, surpassing the standard empirical ladder-entangler ansatz in performance. Overall, our approach can be used as effective state preparation providing a promising route for designing efficient variational quantum circuits for large molecular systems.

quant-ph↗

arXiv2023

Mapping of Hückel Zigzag Carbon Nanotubes onto independent Polyene chains: application to periodic Nanotubes

The electric polarizability and the spread of the total position tensors are used to characterize the metallic vs insulator nature of large (finite) systems. Finite clusters are usually treated within the open boundary condition formalism. This introduces border effects, which prevents a fast convergence to the thermodynamic limit and which can be eliminated within the formalism of periodic boundary conditions. Recently, we have introduced an original approach to periodic boundary conditions, named Clifford Boundary Conditions. It considers a finite fragment extracted from a periodic system and the modification of its topology into that of a Clifford Torus. The quantity representing the position is modified in order to fulfill the system periodicity. In this work, we apply the formalism of Clifford Boundary Conditions to the case of Carbon Nanotubes, whose treatment results to be particularly simple for the Zigzag geometry. Indeed, we demonstrate that at the Hückel level these nanotubes, either finite or periodic, are formally equivalent to a collection of {\em non-interacting dimerized linear chains}, thus simplifying their treatment. This equivalence is used to describe some nanotube properties as the sum of the contributions of the independent chains and to identify the origin of peculiar behaviors (such as the conductivity). Indeed, if the number of hexagons along the circumference is a multiple of three a metallic behavior is found, namely a divergence of both the (per electron) polarizability and total position spread of at least one linear chain. These results are in agreement with those in the literature from Tight-Binding calculations.

cond-mat.mes-hall↗

arXiv2022

A unique one-body position operator for periodic systems

In this work we proof that the one-body position operator for periodic systems that we have recently proposed [Phys. Rev. B 99, 205144] is unique modulo a phase factor and an additive constant. The proof uses several general physical constraints that a periodic one-body position operator should satisfy. We show that these constraints are sufficient to uniquely define a position operator that is compatible with periodic boundary conditions.

cond-mat.other↗

arXiv2021

The localization spread and polarizability of rings and periodic chains

The localization spread gives a criterion to decide between metallic versus insulating behaviour of a material. It is defined as the second moment cumulant of the many-body position operator, divided by the number of electrons. Different operators are used for systems treated with Open or Periodic Boundary Conditions. In particular, in the case of periodic systems, we use the complex-position definition, that was already used in similar contexts for the treatment of both classical and quantum situations. In this study, we show that the localization spread evaluated on a finite ring system of radius $R$ with Open Boundary Conditions leads, in the large $R$ limit, to the same formula derived by Resta et al. for 1D systems with periodic Born-von Kármán boundary conditions. A second formula, alternative to the Resta's one, is also given, based on the sum-over-state formalism, allowing for an interesting generalization to polarizability and other similar quantities.

cond-mat.other↗

arXiv2017

A Jeziorski-Monkhorst fully uncontracted Multi-Reference perturbative treatment I: principles, second-order versions and tests on ground state potential energy curves

The present paper introduces a new multi-reference perturbation approach developed at second order, based on a Jeziorsky-Mokhorst expansion using individual Slater determinants as perturbers. Thanks to this choice of perturbers, an effective Hamiltonian may be built, allowing for the dressing of the Hamiltonian matrix within the reference space, assumed here to be a CAS-CI. Such a formulation accounts then for the coupling between the static and dynamic correlation effects. With our new definition of zeroth-order energies, these two approaches are strictly size-extensive provided that local orbitals are used, as numerically illustrated here and formally demonstrated in the appendix. Also, the present formalism allows for the factorization of all double excitation operators, just as in internally contracted approaches, strongly reducing the computational cost of these two approaches with respect to other determinant-based perturbation theories. The accuracy of these methods has been investigated on ground-state potential curves up to full dissociation limits for a set of six molecules involving single, double and triple bond breaking. The spectroscopic constants obtained with the present methods are found to be in very good agreement with the full configuration interaction (FCI) results. As the present formalism does not use any parameter or numerically unstable operation, the curves obtained with the two methods are smooth all along the dissociation path.

physics.chem-ph↗

arXiv2016

Multi-reference perturbation theory with Cholesky decomposition for the density matrix renormalization group

We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess in a study of a heme model the accuracy of the strongly- and partially-contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex.

physics.chem-ph↗