Extended Hubbard Model in the Dimer Representation. I. Dimer Hamiltonian in the Large U Limit

Abstract

W e consider t he extended H ubb ard mo del for the single cubic lattice and re w rite it in the form of interacting dimers , using the exact solutio n of the dimer problem . W e anal ytical l y deri ve the second quanti zation form of the dimer H amiltoni an elimina tin g from the consideratio ns uno ccupie d dimer energy levels in the large U limit (it is the only assumption ). T he resulting dimer H amiltonian w ritten with the use of the Hubbard op erators and spin operators contains three terms, visuali zin g explicitl y comp eting magnetic interactions (f erromagnetic, antif erromagnetic) as a generaliz atio n of the t { J mo del. T he presented, nonp erturbati ve metho d, can in principl e b e applied to the cluster of any size (e.g. one central atom and z its nearest neighb ours). T he use of the pro j ection technique can further b e appli ed in the case of a crystal to obtain the second quantization form of the extended H ubbard mo del for the sc lattice in the large U limit.

Interference of Particles with Fermionic Internal Degrees of Freedom

“…The term proportional to describes the on-site Coulomb interaction. Additionally, the term involving extends the Hubbard model [ 2 ] by incorporating a spin-dependent inter-site Coulomb interaction [ 15 , 16 ]. As the Hubbard model [ 2 ] is specifically designed to describe systems that exhibit both electronic (transport) and magnetic (spin) properties, it is pertinent to mention describing the z -component of spin operator of each of the dimer sites.…”