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arXiv:cond-mat/0110308

Perturbative expansion using variational phonon basis for Holstein model

Jayita Chatterjee, A. N. Das, P. Choudhury

Published Oct 16, 2001• 0 citations
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Abstract

A simple variational displacement phonon basis, obtained through the modified Lang-Firsov (MLF) transformation, is proposed to study the Holstein model.This phonon basis contains only one variational parameter, but capable of describing lattice distortions at distant sites from the charge carrier. Perturbation method based on this MLF basis is employed to calculate the single-electron ground-state energy and static charge-lattice deformation correlation as a function of electron-phonon coupling. The energy obtained up to the second-order perturbation within this approach agrees well with the available numerical results for the entire range of coupling strength.

DOI
10.48550/arxiv.cond-mat/0110308

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A simple variational displacement phonon basis, obtained through the modified Lang-Firsov (MLF) transformation, is proposed to study the Holstein model.This phonon basis contains only one variational parameter, but capable of describing lattice distortions at distant sites from the charge carrier. Perturbation method based on this MLF basis is employed to calculate the single-electron ground-state energy and static charge-lattice deformation correlation as a function of electron-phonon coupling. The energy obtained up to the second-order perturbation within this approach agrees well with the available numerical results for the entire range of coupling strength.
The two-site two-electron Holstein model is studied within a perturbation method based on a variational phonon basis obtained through the modified Lang-Firsov (MLF) transformation. The ground-state wave function and the energy are found out considering up to the seventh and eighth order of perturbation, respectively. The convergence of the perturbation corrections of different orders to the ground state energy as well as to different correlation functions are investigated. The kinetic energy and the correlation functions involving charge and lattice deformations are studied as a function of electron-phonon (eee-ph) coupling for different values of adiabaticity parameter and Coulomb repulsion. The simultaneous effect of the eee-ph coupling and Coulomb repulsion on the kinetic energy shows interesting features.
The single-electron energy and static charge-lattice deformation correlations have been calculated for the first excited state of a two-site Holstein model within perturbative expansions using different standard phonon bases obtained through Lang-Firsov (LF) transformation, LF with squeezed phonon states, modified LF, modified LF transformation with squeezed phonon states, and also within weak-coupling perturbation approach. Comparisons of the convergence of the perturbative expansions for different phonon bases reveal that modified LF approach works much better than other approaches for major range of the coupling strength.
The single-electron energy and static charge-lattice deformation correlations have been calculated for the first excited state of a two-site Holstein model within perturbative expansions using different standard phonon bases obtained through Lang–Firsov (LF) transformation, LF with squeezed phonon states, modified LF, modified LF transformation with squeezed phonon states, and also within weak-coupling perturbation approach. Comparisons of the convergence of the perturbative expansions for different phonon bases reveal that modified LF approach works much better than other approaches for major range of the coupling strength.
The two-site single-polaron problem is studied within perturbative expansions using different standard phonon bases obtained through Lang-Firsov (LF), modified LF, and modified LF transformations with squeezed phonon states. The role of these convergent expansions using the above prescriptions in lowering the energy and in determining the correlation functions are compared for different values of the coupling strength. The single-electron energy, oscillator wave functions, and correlation functions are calculated for the same system. The applicability of different phonon bases in different regimes of the coupling strength, as well as in different regimes of hopping, is also discussed.
We look for an analytical method which can describe the Holstein model over the entire region of electron–phonon (e–ph) coupling strength. Considering a toy model of two sites the perturbation expansions are developed for the Holstein Hamiltonian using different standard phonon bases. It is found that the modified Lang Firsov phonon basis shows satisfactory convergence for almost the entire range of e–ph coupling from the antiadiabatic limit to the intermediate range of hopping. This method is used to study the magnetic transition and the small to large polaron crossover in a double exchange model with e–ph interaction. Implications of the results in the context of manganites are discussed.