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arXiv:2509.20188

Solution of the Anderson chain with two-particle hybridization of localized and itinerant electrons

Igor N. Karnaukhov

Published Sep 24, 2025• 0 citations
arXivHTMLPDF

Abstract

A modified Anderson lattice is proposed, whose the Hamiltonian accounts for the two-particle hybridization of localized and itinerant electrons instead of one-particle hybridization which takes into account in the original Anderson model. The 1D version of this model can be solved using the Bethe ansazt. It has been shown that hybridization between itinerant and frozen localized electrons results in an effective on-site interaction between itinerant electrons. The magnitude and sign of this interaction depend on the position of the level relative to the Fermi energy (the energy of this level corresponds to the two-particle state of localized electrons at a site). It is shown that when the energy of an localized electron in the two-particle state lies above the Fermi energy, the effective on-site interaction between itinerant electrons is attractive. A repulsive interaction between itinerant electrons occurs when this energy lies below the Fermi energy. Thus, two-part hybridization between localized and itinerant electrons can lead to effective attraction between itinerant electrons, which is unique in itself and may underlie the nature of high-temperature superconductivity.

DOI
10.48550/arxiv.2509.20188

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Some ground state properties of a fermion system are investigated. An initial Hamiltonian being a generalization of the lattice Anderson model describes this system as a two-band electron-phonon one where both of electron bands are narrow (one is wider than the other). Two bands are hybridized and electrons from both of them are strongly coupled to the same local phonons. After performing the Lang–Firsov type transformation, a new polaron Hamiltonian is obtained. As a result, there appear three effective polaron-polaron interactions in this Hamiltonian and the bandwidths of both of electron bands are reduced. It is assumed that the reduction of the bandwidth of one of the bands is sufficiently strong to make this band dispersionless. Each of the interactions can lead to superconductivity on its own but only one of them is taken into account at this stage; it is the interaction between electrons from the band with a dispersion. The Bogolyubov’s mean field approach is used in order to find the spectrum of the reduced effective Hamiltonian. The effect of the hybridization on the superconducting gap and the relationship between the critical hybridization and the average number of electrons from the wider band per lattice site are investigated.
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