Electronic and phononic states of the Holstein-Hubbard dimer of variable length

Abstract

We consider a model Hamiltonian for a dimer of length a including all the electronic one-and twobody terms consistent with a single orbital per site, a free Einstein phonon term for a frequency Ω, and an electron-phonon coupling g0 of the Holstein type. The bare electronic interaction parameters were evaluated in terms of Wannier functions built from Gaussian atomic orbitals. An effective polaronic Hamiltonian was obtained by an unrestricted displaced-oscillator transformation, followed by evaluation of the phononic terms over a squeezed-phonon variational wave function. For the cases of quarter-filled and half-filled orbital, and over a range of dimer length values, the ground state for given g0 and Ω was identified by simultaneously and independently optimizing the orbital shape, the phonon displacement and the squeezing effect strength. As a varies, we generally find discontinuous changes of both electronic and phononic states, accompanied by an appreciable renormalization of the effective electronic interactions across the transitions, due to the equilibrium shape of the wave functions strongly depending on the phononic regime and on the type of ground state. 71.38.+i, 31.90.+s

Distance-Depending Electron-Phonon Interactions From One- And Two-Body Electronic Terms in a Dimer

“…We shall develop both the one-(ǫ, t) and two-body(X, U, V, J z = J xy = P ) electron interaction parameters, evaluated as in Ref. 1, by assuming a non-degenerate orbital described by Wannier functions built from atomic orbitals of Gaussian shape. We associate to each site a Gaussian atomic-like orbital φ i (r − R i ), with the ions centered at the positions R i ≡ (±a/2 + u i , 0, 0) (i = 1, 2) .…”

“…So, to obtain the corresponding couplings, one can simply take the derivative with respect to a of the parameters in Eq.1 as evaluated in Ref. 1.…”

Two-site two-electron generalized Hubbard–Holstein model: a perturbation study

“…To examine that whether this perturbation method based on MLF phonon basis works well or not with increasing number of electrons and in presence of electron-electron (e-e) interaction, we consider a two-site two-electron Holstein model which is the minimal model to investigate the effect of e-e interaction on the polaronic properties and the combined effects of the electronic correlation and the e-ph coupling on the kinetic energy of the system. It may be mentioned that the polaron crossover has been studied in two-site and four-site systems in presence of e-e interaction by different groups [6,7,8] with the Holstein model previously. But most of the studies were done at the zero phonon approximation level with MLF or MLFS transformed Hamiltonian.…”

Nonlinear optical properties of the active medium in intracavity phase conjugation of the radiation of a pulsed electron-beam-controlled discharge CO2laser. I. Experiments

“…Ground state properties [9][10][11][12][13] along with spectral properties [16,9,14,15] have been studied using both numerical [9,14,10] as well as analytical methods [16,12,13]. Also for its simplicity, the two-site cluster has been studied in more involved problems, such as polaron formation in the presence of double exchange [17] or in the presence of on-site electronic repulsion [18]. It is worth mentioning also the relevance of the two-site system in the high temperature case, where the coherence is lost in a single tunnelling [19].…”