Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics B

A CONVERGENT PERTURBATION METHOD FOR THE HOLSTEIN MODEL AND ITS APPLICATION TO THE DOUBLE EXCHANGE SYSTEM

A. N. Das, Jayita Chatterjee, M. MITRA

Published Aug 10, 2001• 1 citation
Publisher

Abstract

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.

DOI
10.1142/s0217979201006513

Related papers

TWO-SITE POLARON PROBLEM: A PERTURBATION APPROACH WITH VARIATIONAL BASIS STATES

A. N. Das, JAYITA CHATTERJEE

A convergent perturbation method using modified Lang Firsov transformation is developed for a two-site single-polaron system. The method is applicable for the entire range of the electron–phonon coupling strength from the antiadiabatic limit to the intermediate region of hopping. The single-electron energies, oscillator wavefunctions and correlation functions, calculated using this method, are in good agreement with the exact results.

arXiv:cond-mat/9905373•International Journal of Modern Physics B•Dec 30, 1999•14 citations

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

Jayita Chatterjee, A. N. Das

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.

arXiv:cond-mat/9908172•Physical review. B, Condensed matter•Feb 15, 2000•28 citations

Two-site polaron problem: a perturbation approach with variational basis states

A. N. Das, Jayita Chatterjee

A convergent perturbation method using modified Lang Firsov transformation is developed for a two-site single-polaron system. The method is applicable for the entire range of the electron-phonon coupling strength. The single-electron energies, oscillator wave functions and correlation functions, calculated using this method, are in good agreement with the exact results. 2

•Jan 1, 1999•13 citations

Perturbative expansion using variational phonon basis for Holstein model

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

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.

arXiv:cond-mat/0110308•Oct 16, 2001•0 citations

Role of disorder in the two-site Holstein model with double exchange

Jayita Chatterjee

Using the perturbation method based on a variational phonon basis obtained by the modified Lang-Firsov (MLF) transformation, the two-site double-exchange Holstein model is studied in presence of a finite difference in bare site energies (ǫd=ǫ2-ǫ1). The polaronic ground-state wave function is calculated up to the fifth order of perturbation. The effect of ǫd (acts as a site-energy disorder) on the polaron crossover, polaronic kinetic energy and polaron localization are studied. Role of disorder on the properties of the double-exchange system is discussed.

•Jan 1, 2015•0 citations

Crossover between large and small polarons in many-electron system with on-site repulsion

Hongxing Zheng

An analytical approach has been developed for the electron–phonon coupling in the Holstein–Hubbard model. The Hubbard U is treated approximately by the slave-boson approach. We show that our approach is flexible and physically clear because it is based on perturbation theory. When the dimensionless ratio ω p /2 Dt is small, ω p /2 Dt ≪ 1, our result is similar to that of the Migdal–Eliashberg theory. When ω p /2 Dt > 1, our result approaches that of the Lang–Firsov transformation and small polaron theory. We have calculated the effective mass of electrons at the Fermi surface to show that the new perturbation approach works well in the intermediate region where ω p /2 Dt ∼ 1.

Journal of Physics A Mathematical and General•Aug 20, 2003•0 citations
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.
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.
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.
Using the perturbation method based on a variational phonon basis obtained by the modified Lang-Firsov (MLF) transformation, the two-site double-exchange Holstein model is studied in presence of a finite difference in bare site energies (ǫd=ǫ2-ǫ1). The polaronic ground-state wave function is calculated up to the fifth order of perturbation. The effect of ǫd (acts as a site-energy disorder) on the polaron crossover, polaronic kinetic energy and polaron localization are studied. Role of disorder on the properties of the double-exchange system is discussed.
An analytical approach has been developed for the electron–phonon coupling in the Holstein–Hubbard model. The Hubbard U is treated approximately by the slave-boson approach. We show that our approach is flexible and physically clear because it is based on perturbation theory. When the dimensionless ratio ω p /2 Dt is small, ω p /2 Dt ≪ 1, our result is similar to that of the Migdal–Eliashberg theory. When ω p /2 Dt > 1, our result approaches that of the Lang–Firsov transformation and small polaron theory. We have calculated the effective mass of electrons at the Fermi surface to show that the new perturbation approach works well in the intermediate region where ω p /2 Dt ∼ 1.