In this paper we present a general theoretical framework to study interacting electrons under the influence of an external time-periodic driving, such as a homogeneous laser field. This is performed through a true many-body calculation and the use of Floquet theory. In particular, we consider a linear atomic chain using the Hubbard model to describe the short-ranged Coulomb interactions between electrons, plus Cluster Perturbation Theory to embed the many-body exact solution for a finite system into both an extended and an infinite lattice. Due to the presence of the external time-periodic perturbation, the electronic problem can be mapped into the study of photon-dressed quasiparticles thanks to Floquet theorem, keeping into account of all the virtual processes (absorption and emission of photons by electrons) with the laser field. This leads to an extension of the many-body static theories to out-of-equilibrium systems. This theoretical approach allowed us to show how the electronic properties of the system can be controlled and tuned varying the laser parameters. Above all, an inverse insulator-to-metal transition can be obtained for the one dimensional infinite lattice, and edge localized states appear as a finite size effect in an extended truncated chain.In this paper we present a general theoretical framework to study interacting electrons under the influence of an external time-periodic driving, such as a homogeneous laser field. This is performed through a true many-body calculation and the use of Floquet theory. In particular, we consider a linear atomic chain using the Hubbard model to describe the short-ranged Coulomb interactions between electrons, plus Cluster Perturbation Theory to embed the many-body exact solution for a finite system into both an extended and an infinite lattice. Due to the presence of the external time-periodic perturbation, the electronic problem can be mapped into the study of photon-dressed quasiparticles thanks to Floquet theorem, keeping into account of all the virtual processes (absorption and emission of photons by electrons) with the laser field. This leads to an extension of the many-body static theories to out-of-equilibrium systems. This theoretical approach allowed us to show how the electronic properties of the system can be controlled and tuned varying the laser parameters. Above all, an inverse insulator-to-metal transition can be obtained for the one dimensional infinite lattice, and edge localized states appear as a finite size effect in an extended truncated chain.

Journal of Physics Conference SeriesMay 1, 20170 citations

Pair-Correlation Effects in Many-Body Systems

Kristian Blom

Springer thesesJan 1, 20233 citations

Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods

Raphaël Photopoulos, Antoine Boulet

Introducing low-energy effective Hamiltonians is usual to grasp most correlations in quantum many-body problems. For instance, such effective Hamiltonians can be treated at the mean-field level to reproduce some physical properties of interest. Employing effective Hamiltonians that contain many-body correlations renders the use of perturbative many-body techniques difficult because of the overcounting of correlations. In this work, we develop a strategy to apply an extension of the many-body perturbation theory starting from an effective interaction that contains correlations beyond the mean-field level. The goal is to re-organize the many-body calculation to avoid the overcounting of correlations originating from the introduction of correlated effective Hamiltonians in the description. For this purpose, we generalize the formulation of the Rayleigh-Schrödinger perturbation theory by including free parameters adjusted to reproduce the appropriate limits. In particular, the expansion in the bare weak-coupling regime and the strong-coupling limit serves as a valuable input to fix the value of the free parameters appearing in the resulting expression. This method avoids double counting of correlations using beyond-mean-field strategies for the description of many-body systems. The ground state energy of various systems relevant for ultracold atomic, nuclear, and condensed matter physics is reproduced qualitatively beyond the domain of validity of the standard many-body perturbation theory. Finally, our method suggests interpreting the formal results obtained as an effective field theory using the proposed reorganization of the many-body calculation. The results, like ground state energies, are improved systematically by considering higher orders in the extended many-body perturbation theory while maintaining a straightforward polynomial expansion.Introducing low-energy effective Hamiltonians is usual to grasp most correlations in quantum many-body problems. For instance, such effective Hamiltonians can be treated at the mean-field level to reproduce some physical properties of interest. Employing effective Hamiltonians that contain many-body correlations renders the use of perturbative many-body techniques difficult because of the overcounting of correlations. In this work, we develop a strategy to apply an extension of the many-body perturbation theory starting from an effective interaction that contains correlations beyond the mean-field level. The goal is to re-organize the many-body calculation to avoid the overcounting of correlations originating from the introduction of correlated effective Hamiltonians in the description. For this purpose, we generalize the formulation of the Rayleigh-Schrödinger perturbation theory by including free parameters adjusted to reproduce the appropriate limits. In particular, the expansion in the bare weak-coupling regime and the strong-coupling limit serves as a valuable input to fix the value of the free parameters appearing in the resulting expression. This method avoids double counting of correlations using beyond-mean-field strategies for the description of many-body systems. The ground state energy of various systems relevant for ultracold atomic, nuclear, and condensed matter physics is reproduced qualitatively beyond the domain of validity of the standard many-body perturbation theory. Finally, our method suggests interpreting the formal results obtained as an effective field theory using the proposed reorganization of the many-body calculation. The results, like ground state energies, are improved systematically by considering higher orders in the extended many-body perturbation theory while maintaining a straightforward polynomial expansion.

arXiv:2402.17627SciPost PhysicsJan 6, 20250 citations

ASPECTS OF MANY-BODY PERTURBATION THEORY

WORLD SCIENTIFIC eBooksFeb 19, 20190 citations

Functional representation of correlations in inhomogeneous many-electron systems

Klaus Dietz, Bernd Artur Heß

We discuss the Legendre conjugate of the Hohenberg-Kohn energy-density functional, i.e., the total energy of an inhomogeneous many-electron system, considered as a functional of the external Coulomb potential (the nuclear Coulomb skeleton of a molecule, for instance) as the starting point of an alternative formulation of a theory of electronic correlations. We then relate this functional to the nonrelativistic or relativistic microscopic many-body theory. The essential bridge between the two theories is many-body perturbation theory perturbing around a mean field. We then point out that a particular choice for the latter, the g-Hartree mean field, leads to a transparent physical picture: The relevant functional of the external field, ${g}_{0}$ -1, representing electronic correlations, is interpreted as a polarization charge density induced by the latter. This picture, in turn, leads to a Clausius-Mosotti type of equation for this correlation functional. Applications to atomic- and molecular-structure calculations are discussed.We discuss the Legendre conjugate of the Hohenberg-Kohn energy-density functional, i.e., the total energy of an inhomogeneous many-electron system, considered as a functional of the external Coulomb potential (the nuclear Coulomb skeleton of a molecule, for instance) as the starting point of an alternative formulation of a theory of electronic correlations. We then relate this functional to the nonrelativistic or relativistic microscopic many-body theory. The essential bridge between the two theories is many-body perturbation theory perturbing around a mean field. We then point out that a particular choice for the latter, the g-Hartree mean field, leads to a transparent physical picture: The relevant functional of the external field, ${g}_{0}$-1, representing electronic correlations, is interpreted as a polarization charge density induced by the latter. This picture, in turn, leads to a Clausius-Mosotti type of equation for this correlation functional. Applications to atomic- and molecular-structure calculations are discussed.

Physical Review AMar 1, 19905 citations

Perturbation Theory of Many-Body Systems

Giampaolo Co’

UNITEXT for physicsJan 1, 20260 citations

{g}_{0}

-1, representing electronic correlations, is interpreted as a polarization charge density induced by the latter. This picture, in turn, leads to a Clausius-Mosotti type of equation for this correlation functional. Applications to atomic- and molecular-structure calculations are discussed.