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Momentum exchange in quantum two-electron photon interactions

Suraj Kumar, Jeremy Zhen Jie Lim, Nicholas Rivera, Yee Sin Ang, L. K. Ang, Liang Jie Wong

Published Jan 1, 2023• 0 citations
Publisher

Abstract

We show that multiple electrons become correlated with each other through their interaction with light, even in the absence of Coulombic interactions, providing a way to realize largenumber Fock states on reasonable time scales.
DOI
10.1364/cleo_fs.2023.fth1c.2

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Simulations of interacting electrons and bosons out of equilibrium, starting from first principles and aiming at realistic multiscale scenarios, is a grand theoretical challenge. Here, using the formalism of nonequilibrium Green's functions and relying in a crucial way on the recently discovered time-linear formulation of the Kadanoff-Baym equations, we present a versatile toolbox for the simulation of correlated electron-boson dynamics. A large class of methods are available, from the Ehrenfest to the dressed GDGDGD for the treatment of electron-boson interactions in combination with perturbative, i.e., Hartree-Fock and second-Born, or nonperturbative, i.e., GWGWGW and TTT matrices either without or with exchange effects, for the treatment of the Coulomb interaction. In all cases the numerical scaling is linear in time and the equations of motion satisfy all fundamental conservation laws.
The role of spatial forces, and of Hund's rule (exchange) forces, and the validity of the Hartree-Fock approximation in the band theory of magnetism of metals is reviewed. Some reasonable conjectures which have been made elsewhere by the author and others are examined in the light of an exactly soluble model of interacting electrons in one dimension. It is shown that within the framework of validity of this model, spatial i.e., direct (Coulomb) forces do not influence the spin susceptibility, and conversely, Hund's rule exchange forces do not affect the dielectric constant or plasmon spectrum. It is recalled that the time-independent Hartree-Fock approximation yields an incorrect spectrum of elementary excitations, and it is also shown explicitly that the magnetic susceptibility calculated in this approximation is incorrect. A paradox is noted, concerning whether ``correlations'' can in fact correct the errors in the H-F approximation. Finally, it is shown that when there are only space forces, such spin density waves as might be introduced in to the H-F ground state of the model are in fact spurious, because they are not representative of the correlations which exist in the true ground state.