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

TL;DR

This study models a dimer system incorporating electronic interactions, phonons, and electron-phonon coupling, revealing how varying dimer length causes discontinuous state changes and interaction renormalizations.

Contribution

It introduces a comprehensive approach combining electronic and phononic states with variational methods to analyze dimer systems at different fillings and lengths.

Findings

Discontinuous electronic and phononic state changes with dimer length.

Significant renormalization of electronic interactions across transitions.

Ground state properties depend strongly on phononic regime and filling.

Abstract

We consider a model Hamiltonian for a dimer including all the electronic one- and two-body terms consistent with a single orbital per site, a free Einstein phonon term, and an electron-phonon coupling 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 was identified by simultaneously and independently optimizing the orbital shape, the phonon displacement and the squeezing effect strength. As the dimer length 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.