arXiv subjects

J. Arjan Berger

Publications and source records attributed to J. Arjan Berger.

At least 19 recordsLinked to original sources

arXiv2026

Benchmark of Multi-Channel Dyson Equation and Algebraic Diagrammatic Construction Methods for molecules

The Dyson-algebraic diagrammatic construction (ADC) and the multi-channel Dyson equation (MCDE) formalisms explicitly leverage multi-particle channels to formulate correlated theories of the single-particle Green's function that produce positive semi-definite spectral functions by construction. While the MCDE is strictly rooted in the Dyson formalism, most ADC calculations are performed in the non-Dyson (nD) framework that decouples electron attachment and detachment sectors. We benchmark the Dyson-ADC(2)-X [that is equivalent to the (3,1)-MCDE] and ADC(3) approximations on a set of 58 ionization potentials of 23 small molecules for which near-full configuration interaction reference data exist. Comparison of Dyson- to nD-ADC(3) reveals deviations of the order of 0.1 eV between both methods, calling into question the reliability of the nD approximation. We show that Dyson-ADC gives similar accuracy for first IPs as for semi-valence and semi-core transitions. Finally, we also benchmark the screened (3,1)-MCDE that screens all ladder interactions, and show that it improves over its unscreened counterpart.

physics.chem-ph↗

arXiv2026

Direct and inverse photoemission spectra from the screened multichannel Dyson equation

We present the screened multichannel Dyson equation for the simulation of both direct and inverse photoemission spectra from first principles. The screened multichannel Dyson equation improves upon the standard multichannel Dyson equation by correctly including the screening of all particle-particle and electron-hole interactions due to the presence of the other electrons. Using the example of bulk silicon, we demonstrate that the screened multichannel Dyson equation can capture the main features of the direct and inverse photoemission spectra. In particular, it captures the correct position of the silicon plasmon satellite, unlike standard many-body approaches such as $GW$, which strongly overestimates the binding energy of this satellite. Finally, we show that also the standard multichannel Dyson equation and the second-Born approximation strongly overestimate the binding energy of the plasmon satellite, thus demonstrating the importance of properly screening all particle-particle and electron-hole interactions.

cond-mat.other↗

arXiv2026

Core and valence photoemission spectra of atoms and molecules from a multichannel Dyson equation

We recently presented multichannel Dyson equations for the \textit{ab initio} simulation of various spectroscopies. In particular, we introduced a multichannel Dyson equation for the description of photoemission spectra. In this work, we apply our approach to the simulation of photoemission spectra of atoms and molecules. We introduce a numerically efficient approach to calculate their spectral functions. We compare the spectra obtained within the multichannel Dyson equation to those obtained with full configuration interaction and the $GW$ method. We are thus able to show that the satellite features due to shake-up processes are significantly better described by the multichannel Dyson equation than by $GW$. Finally, we also discuss the slow convergence of the satellite energies with the size of the basis set and we propose a simple extrapolation method to reach the complete basis-set limit.

cond-mat.other↗

arXiv2026

Algebraic Diagrammatic Construction of the Multichannel Dyson Equation

The multichannel Dyson equation (MCDE) was recently introduced as a new approximation scheme to compute the one-body Green function in many-body systems, as reported by Riva et al. in Physical Review Letters, volume 131, article 216401, published in 2023. The physical content of this novel approximation scheme is further clarified by recovering it from an extended version of the algebraic diagrammatic construction (ADC) truncation scheme. It is thus demonstrated that the MCDE approximation lies in between the so-called ADC(2) and ADC(3) truncations of the dynamical self energy. Building on this clarification, the MCDE approximation is tested on the periodic one-dimensional Hubbard model with 4, 6, and 8 site lattices and shown to deliver an improved treatment over ADC(2) of both the quasiparticle peaks and the so-called satellites in the spectral strength distribution.

cond-mat.str-el↗

arXiv2026

The multichannel Dyson equation for double ionisation spectroscopies

Several photoemission spectroscopies and, in particular, Auger spectroscopy, involve double-ionization processes. For the numerical simulation of these spectroscopies it is convenient to use the particle-particle channel of the two-body Green's functions since its poles correspond to excitation energies in which the final state has two more particles (holes or electrons) than the initial state. In standard approaches it is approximated within the random phase approximation. As a consequence only the quasiparticles of the photoemission spectrum are captured but none of the satellites features. In this work, we go beyond this approximation by employing the multichannel Dyson equation. By coupling the particle-particle two-body Green's function to the 3-hole-1-electron and 3-electron-1-hole channels of the four-body Green's function, the multichannel Dyson equation incorporates correlations beyond the RPA in a straightforward way. We are thus able to describe both quasiparticles and satellites in the photoemission spectra.

cond-mat.str-el↗

arXiv2025

Quantum chemistry for solids made simple on the Clifford torus

We present a general theory to treat periodic solids with quantum-chemistry methods. It relies on two main developments: 1) the modeling of a solid as a Clifford torus which is a torus that is both periodic and flat and 2) the introduction of a periodic gaussian basis set that is compatible with the topology of the Clifford torus. We illustrate our approach by calculating the ground-state energy of a periodic chain of hydrogen atoms within both Hartree-Fock and coupled cluster theory. We demonstrate that our approach yields the correct ground-state energy in the thermodynamic limit by comparing it to the ground-state energy of a ring of hydrogen atoms in the same limit. Since equivalent ring-like calculations for three-dimensional solids are impossible, our approach is an excellent alternative to perform quantum-chemistry calculations of solids. Our Clifford formalism can be seamlessly combined with current implementations of quantum-chemistry methods designed for atoms and molecules to make them applicable to solids.

quant-ph↗

arXiv2025

Ground and excited-state properties of the extended Hubbard dimer from the multichannel Dyson equation

We have recently presented the multichannel Dyson equation as an alternative to the standard single-channel Dyson equation. While the latter involves a single many-body Green's function, the former uses a multichannel Green's function in which two or more many-body Green's functions are coupled. Quasiparticles and satellites are thus naturally treated on equal footing in the multichannel Dyson equation. To assess the accuracy of our approach we apply it here to the ground- and excited-state properties of the extended Hubbard dimer, an exactly solvable model for $H_2$. In particular, we focus on the potential energy surface as well as the corresponding spectral functions and HOMO-LUMO gaps, which are well-known challenges for many-body approximations such as second Born and $GW$. We show that the multichannel Dyson equation gives overall very good results for all properties considered and outperforms both $GW$ and second Born. In particular, the multichannel Dyson equation yields the correct ground-state energy and HOMO-LUMO gap in the dissociation limit contrary to $GW$.

cond-mat.str-el↗

arXiv2025

Multichannel Dyson equations for even- and odd-order Green's functions: application to double excitations

We extend the concept of the multichannel Dyson equation that we have recently derived to model photoemission spectra by coupling the one- and the three-body Green's functions, to higher-order Green's functions and to other spectroscopies. We show the general structure of the equations and how one can systematically approximate the corresponding multichannel self-energy. As a particular case, we focus on the coupling of the two-body and the four-body Green's functions in the electron-hole channel to describe neutral excitations. This formulation allows for the description of important many-body effects, such biexcitons, in a natural way. We illustrate our approach by applying it to a two-level model system, which, in a one-particle picture, exhibits single and double excitations. Our method can correctly describe both kinds of excitation, unlike standard approaches, and in good agreement with the exact results.

cond-mat.str-el↗

arXiv2024

Multichannel Dyson equation: derivation and analysis

In a recent letter [Phys. Rev. Lett. 131, 216401] we presented the multichannel Dyson equation (MCDE) in which two or more many-body Green's functions are coupled. In this work we will give further details of the MCDE approach. In particular we will discuss: 1) the derivation of the MCDE and the definition of the space in which it is to be solved; 2) the rationale of the approximation to the multichannel self-energy; 3) a diagrammatic analysis of the MCDE; 4) the recasting of the MCDE on an eigenvalue problem with an effective Hamiltonian that can be solved using standard numerical techniques. This work mainly focuses on the coupling between the one-body Green's function and the three-body Green's function to describe photoemission spectra, but the MCDE method can be generalized to the coupling of other many-body Green's functions and to other spectroscopies.

nucl-th↗

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

The multi-channel Dyson equation: coupling many-body Green's functions

We present the multi-channel Dyson equation that combines two or more many-body Green's functions to describe the electronic structure of materials. In this work we use it to model photoemission spectra by coupling the one-body Green's function with the three-body Green's function. We demonstrate that, unlike methods using only the one-body Green's function, our approach puts the description of quasiparticles and satellites on an equal footing. We propose a multi-channel self-energy that is static and only contains the bare Coulomb interaction, making frequency convolutions and self-consistency unnecessary. Despite its simplicity, we demonstrate with a diagrammatic analysis that the physics it describes is extremely rich. Finally, we present a framework based on an effective Hamiltonian that can be solved for any many-body system using standard numerical tools. We illustrate our approach by applying it to the Hubbard dimer and show that it is exact both at 1/4 and 1/2 filling.

cond-mat.str-el↗

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↗

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

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↗

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↗

arXiv2022

Photoemission spectral functions from the three-body Green's function

We present an original strategy for the calculation of direct and inverse photo-emission spectra from first principles. The main goal is to go beyond the standard Green's function approaches, such as the $GW$ method, in order to find a good description not only of the quasiparticles but also of the satellite structures, which are of particular importance in strongly correlated materials. To this end we use as a key quantity the three-body Green's function, or, more precisely, its hole-hole-electron and electron-electron-hole parts, and we show how the one-body Green's function, and hence the corresponding spectral function, can be retrieved from it. We show that, contrary to the one-body Green's function, information about satellites is already present in the non-interacting three-body Green's function. Therefore, simple approximations to the three-body self-energy, which is defined by the Dyson equation for the three-body Green's function and which contains many-body effects, can still yield accurate spectral functions. In particular, the self-energy can be chosen to be static which could simplify a self-consistent solution of the Dyson equation. We give a proof of principle of our strategy by applying it to the Hubbard dimer, for which the exact self-energy is available.

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↗

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↗