On the derivation of the t-J model: electron spectrum and exchange interactions in narrow energy bands

TL;DR

This paper derives the t-J model from a many-electron Hamiltonian considering atomic wave function non-orthogonality, revealing asymmetries in Hubbard subbands and indirect exchange interactions affecting magnetism in narrow bands.

Contribution

It introduces a derivation of the t-J model that accounts for non-orthogonality of atomic orbitals, highlighting effects on electron spectrum and magnetic interactions.

Findings

Asymmetry of Hubbard subbands in nearly half-filled bands.

Non-orthogonality leads to indirect antiferromagnetic exchange.

Implications for magnetism in narrow and frustrated lattices.

Abstract

A derivation of the t-J model of a highly-correlated solid is given starting from the general many-electron Hamiltonian with account of the non-orthogonality of atomic wave functions. Asymmetry of the Hubbard subbands (i.e. of ``electron'' and ``hole''cases) for a nearly half-filled bare band is demonstrated. The non-orthogonality corrections are shown to lead to occurrence of indirect antiferromagnetic exchange interaction even in the limit of the infinite on-site Coulomb repulsion. Consequences of this treatment for the magnetism formation in narrow energy bands are discussed. Peculiarities of the case of ``frustrated'' lattices, which contain triangles of nearest neighbors, are considered.