Investigation of on-site interorbital single-electron hoppings in general multiorbital systems

Abstract

A general multi-orbital Hubbard model, which includes on-site inter-orbital electron hoppings, is introduced and studied. It is shown that the on-site inter-orbital single electron hopping is one of the most basic interactions. Two electron spin-flip and pair-hoppings are shown to be correlation effects of higher order than the on-site inter-orbital single hopping. It is shown how the double and higher hopping interactions can be well-defined for arbitrary systems. The two-orbital Hubbard model is studied numerically to demonstrate the influence of the single electron hopping effect, leading to a change of the shape of the bands and a shrinking of the difference between the two bands. Inclusion of the on-site inter-orbital hopping suppresses the so-called orbital-selective Mott transition.PACS numbers: 71.10.Fd, 71.27.+a, 71.30.+h Strongly correlated electron systems have drawn great interest, as they exhibit many exotic phenomena, such as metal-insulator transitions, unusual forms of magnetism, superconductivity, and heavy-fermion behavior.1,2 These systems are therefore investigated theoretically in both model and ab initio calculations. One of the most essential tasks is to model the system appropriately, i.e., such that a realistic physical picture can be attained. In condensed matter theory the Hubbard model, which was originally proposed in the early sixties, 3-5 is one of the simplest, yet also the most important and most frequently studied lattice model to investigate strongly correlated electron systems. It sets up a competition between an inter-site quantum mechanical hopping term and an on-site Coulomb interaction term. As a consequence the model can describe various non-trivial phenomena. Due to its simplicity and because the model has captured the essence of strongly correlated electron systems, the Hubbard model has been widely used. 6-9In a realistic situation an atom in a correlated system will usually have several partial filled orbitals and should therefore be described with a multi-orbital (MO) Hubbard model. With the inclusion of orbital degrees of freedom, inter-orbital interactions have to be included for such a system. The inter-site hoppings should now be a sum of the inter-site intra-orbital hoppings and the inter-site inter-orbital hoppings, where the two kinds of hopping are defined according to the orbital indices of the start and the end orbitals for hopping electron are identical or not, respectively. Moreover, besides the remain competition of the inter-site hopping and on-site Coulomb interactions, one new kind of on-site interactions will join into this competition, i.e., the on-site inter-orbital hoppings. Acting as the inter-site hoppings, the on-site inter-orbital hoppings are also associated to the kinetic energy of electrons. All the inter-site hoppings, on-site inter-orbital hoppings and on-site Coulomb interactions (which also divides as on-site intra-orbital Coulomb interactions and on-site inter-orbital Coulomb interactions) constitute a competition for various inter...

The role of electron–vibron interaction and local pairing in conductivity and superconductivity of alkali-doped fullerides

“…where V c (r, r ) is a operator of on-site Coulomb interaction. In a multi-orbital system the on-site Coulomb interaction is presented with two terms: density-density interaction energy U (U for different orbitals) and the energy of the double inter-orbital hoppings ll mm σσ J l m lm a + il σ a + im σ a ilσ a imσ (where l = l, m = m) [29]. The hoppings' energy cannot be reduced to the multiplication of operators of occupation numbers like the density-density energy U lm σσ n ilσ n imσ .…”

Non-equilibrium magnetic interactions in strongly correlated systems

“…where ĤT (t) is the single-particle Hamiltonian, including the time-dependent field, and ĤV is the (time-independent) interaction potential between the electrons. We will treat a multi-band Hubbard model [27,41], therefore the electronic single-particle states are identified by three labels: the site index i, the orbital index λ and the spin index σ. We ignore spin-orbit coupling and assume that the external field is diagonal in spin indices (we are therefore excluding magnetic fields, but including purely electric fields which are relevant for modelling all-optical experiments).…”

Multiorbital electronic correlation effects of Co adatoms on graphene: An ionic Hamiltonian approach

“…In out-of-equilibrium situations, adequate approximations are necessary to describe the system properties. The most commonly used are probably the noncrossing and one-crossing approximations (NCA and OCA) [27][28][29], although the equations of motion (EOM) approach [30,31], used in the present work, provides a useful alternative [32][33][34][35]. In this context, the Co on graphene system was solved at several temperatures by using the GGA+OCA method [8] and recently by using both QMC and ED [11].…”