Stability and nature of polarons in a two-site two-electron model

Two-Site Polaron Problem: A Perturbation Approach With Variational Basis States

“…For our study we consider a two-site one-electron Holstein model for which exact results are available [4]. Previously, we [9,10] investigated the ground state energy and the nature of polarons in a two-site and a four-site Holstein model using the modified Lang Firsov (modified LF) transformation and two-phonon coherent states and found that the energy obtained within such method is very close to the exact result. In this work we develop a perturbation expansion within the modified LF transformation and show that this expansion converges for the entire range of the coupling strength from the antiadiabatic limit to the intermediate region of hopping.…”

Comparison of perturbative expansions using different phonon bases for the two-site Holstein model

“…In this paper we have extended our previous work by calculating up to fifth order perturbation correction to the wave function and sixth order correction to the energy for the ground state of the two-site single polaron system using various standard phonon basis obtained through the LF, modified LF (MLF) and modified LF with squeezing transformations (MLFS). It may be mentioned that the role of squeezing is believed to be important for intermediate coupling and hopping regime [11][12][13][14][15] and studies on a two-site and a four-site Holstein model using the MLFS transformation followed by zero phonon averaging [14,15] show that the energy obtained within such method is very close to the exact result.…”

“…H d represents an effective e-ph system where phonons directly couple with the electronic degrees of freedom and its solution by any analytical method is a non trivial problem. We now use the MLF transformation where the lattice deformations produced by the electron are treated as variational parameters [12,14,17]. For the present system,H…”

“…Now one has to make a proper choice of λ and α so that the perturbative expansion becomes convergent. Usually, within the MLF and MLFS approach zero phonon averaging is made [12,14] and the variational parameters λ and α are found out by minimizing the ground state energy of the system. This corresponds to the minimization of the unperturbed energy in our calculation.…”

“…Such a retardation becomes very important with smaller e-ph coupling strength and larger hopping. The phonon basis chosen in the MLF or MLFS approach have variational displacements and can produce the retardation effect even in the zeroth order of perturbation [12,14]. The ground state energy predicted within the MLF and MLFS method in the zeroth order of perturbation is much lower than that within the LF approach [15] except for large values of the coupling strength, where all the methods become equivalent.…”