Alternating chain with Hubbard-type interactions: renormalization group analysis

TL;DR

This paper applies renormalization group analysis to an alternating chain with Hubbard-like interactions, focusing on a model inspired by the CuO3 chain, to explore phase diagrams and effects of interactions in a two-band system.

Contribution

It introduces a renormalization group approach to analyze Hubbard-type interactions in an alternating two-band chain, specifically modeling the CuO3 chain structure.

Findings

Phase diagrams depend on renormalized couplings and filling levels.

The model captures the effects of on-site and inter-site interactions.

Results are relevant for understanding correlated electron behavior in CuO3 chains.

Abstract

The canonical transformation diagonalizing the one-particle tight binding Hamiltonian for an alternating chain with two non-equivalent sites per unit cell has been used to introduce the Hubbard-like interactions (on-site, inter-site, bond-site and intra-bond) in the corresponding two-band model. The considerations have been restricted to the particular case, suggested by the undistorted 3/4-filled $CuO_{3}$ chain, where the alternating structure comes only from non-equal on-site atomic energies and the gap between the two bands is sufficiently large. The renormalization group method has been then applied to the upper band of this model and the corresponding phase diagram has been analyzed in terms of some renormalized (density dependent) Hubbard-type couplings for arbitrary filling of the upper band. The particular case of $CuO_{3}$ chain is also discussed and the corresponding phase diagram has been drawn in terms of the original (and realistic) coupling constants.