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

Chatterjee, Jayita; Das, Anindita

doi:10.1103/physrevb.61.4592

Cited by 27 publications

(20 citation statements)

References 22 publications

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“…MLF improves the convergence of the 1/λ perturbation series by introducing a suitable variational parameter λ q in the LF transformation, Eq. ( 166), as (Chatterjee and Das , 2000;Chatterjee et al , 2003)…”

Section: Effect Of Dispersive Phononsmentioning

confidence: 99%

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Fröhlich polaron and bipolaron: recent developments

2009

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It is remarkable how the Fröhlich polaron, one of the simplest examples of a Quantum Field Theoretical problem, as it basically consists of a single fermion interacting with a scalar Bose field of ion displacements, has resisted full analytical or numerical solution at all coupling since ∼ 1950, when its Hamiltonian was first written. The field has been a testing ground for analytical, semi-analytical, and numerical techniques, such as path integrals, strong-coupling perturbation expansion, advanced variational, exact diagonalisation (ED), and quantum Monte Carlo (QMC) techniques. This article reviews recent developments in the field of continuum and discrete (lattice) Fröhlich (bi)polarons starting with the basics and covering a number of active directions of research. * Electronic address: jozef.devreese@ua.ac.be † Electronic address: a.s.alexandrov@lboro.ac.uk

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Section: Effect Of Dispersive Phononsmentioning

confidence: 99%

“…( 175). Chatterjee and Das (2000) studied the same problem for any coupling within the perturbative expansion combined with MLF, Eq. ( 196), and MLF with a squeezing canonical transformation (Hang , 1988), exp( S), where S = α(d…”

Section: Holstein Model At Any Couplingmentioning

confidence: 99%

Fröhlich polaron and bipolaron: recent developments

2009

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“…For large e-ph coupling the resultant polaron is a small polaron with high effective mass, while for weak coupling it becomes a large polaron having a much lower effective mass for a finite adiabatic parameter. The crossover from a large to a small polaron and the corresponding changes in the polaronic properties in the ground state have been studied for the Holstein model by different groups [4][5][6][7][8][9][10][11][12][13][14] using various methods to enrich our understanding in this field. However, finite temperature study of the properties of polarons and the effect of disorder on polaronic properties are few and needs more attention.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic properties of Holstein polarons and the effects of disorder

Das¹,

Sil²

2008

J. Phys.: Condens. Matter

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The ground state and finite temperature properties of polarons are studied considering a two-site and a four-site Holstein model by exact diagonalization of the Hamiltonian. The kinetic energy, Drude weight, correlation functions involving charge and lattice deformations, and the specific heat have been evaluated as a function of electron-phonon (e-ph) coupling strength and temperature. The effects of site diagonal disorder on the above properties have been investigated. The disorder is found to suppress the kinetic energy and the Drude weight, reduces the spatial extension of the polaron, and makes the large-to-small polaron crossover smoother. Increasing temperature also plays similar role. For strong coupling the kinetic energy arises mainly from the incoherent hopping processes owing to the motion of electrons within the polaron and is almost independent of the disorder strength. From the coherent and incoherent contributions to the kinetic energy, the temperature above which the incoherent part dominates is determined as a function of e-ph coupling strength.

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“…The MLF phonon basis, where the displacements of the oscillators at different sites around an electron are treated variationally, can describe the retardation and a large to small polaron crossover even within simple approximations [33,34]. Recently the convergence of the perturbation series within the LF and the MLF methods has been studied in a two-site Holstein model for the ground state [30] as well as for the first excited state [36]. It was found that: (i) within the MLF method the perturbation corrections are much smaller than those corresponding to the LF method in the range from weak to intermediate e-ph coupling, (ii) the convergence of the perturbation series within the MLF is also much better in that range, (iii) in the strong coupling limit the MLF phonon basis reduces to the LF basis and the LF pertubation method works very well in this limit.…”

Section: Modified Lang-firsov Phonon Basis For the Holstein Modelmentioning

confidence: 99%

Polaron crossover in molecular solids

Zoli

Das

2004

J. Phys.: Condens. Matter

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An analytical variational method is applied to the molecular Holstein Hamiltonian in which the dispersive features of the dimension dependent phonon spectrum are taken into account by a force constant approach. The crossover between a large and a small size polaron is monitored, in one, two and three dimensions and for different values of the adiabatic parameter, through the behavior of the effective mass as a function of the electron-phonon coupling. By increasing the strength of the inter-molecular forces the crossover becomes smoother and occurs at higher e-ph couplings. These effects are more evident in three dimensions. We show that our Modified Lang-Firsov method starts to capture the occurence of a polaron self-trapping transition when the electron energies become of order of the phonon energies. The self-trapping event persists in the fully adiabatic regime. At the crossover we estimate polaron effective masses of order ∼ 5 − 40 times the bare band mass according to dimensionality and value of the adiabatic parameter. Modified Lang-Firsov polaron masses are substantially reduced in two and three dimensions. There is no self-trapping in the antiadiabatic regime.

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

Cited by 27 publications

References 22 publications

Fröhlich polaron and bipolaron: recent developments

Fröhlich polaron and bipolaron: recent developments

Thermodynamic properties of Holstein polarons and the effects of disorder

Polaron crossover in molecular solids

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