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Phonon spectral function of the Holstein polaron

Jan Loos, Martin Hohenadler, Andreas Alvermann, Holger Fehske

Published Jan 1, 2006• 12 citations
OpenAlex

Abstract

The phonon spectral function of the one-dimensional Holstein model is obtained within weak and strong-coupling approximations based on analytical self-energy calculations.The characteristic excitations found in the limit of small charge-carrier density are related to the known (electronic) spectral properties of Holstein polarons such as the polaron band dispersion.Particular emphasis is laid on the different physics occurring in the adiabatic and antiadiabatic regimes, respectively.Comparison is made with a cluster approach exploiting exact numerical results on small systems to yield an approximation for the thermodynamic limit.This method, similar to cluster perturbation theory, confirms the analytical findings, and yields accurate results also in the intermediate-coupling regime.

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Phonon spectral function of the Holstein polaron

J Loos, M Hohenadler, A Alvermann +1 more

The phonon spectral function of the one-dimensional Holstein model is obtained within weak and strong-coupling approximations based on analytical self-energy calculations. The characteristic excitations found in the limit of small charge-carrier density are related to the known (electronic) spectral properties of Holstein polarons such as the polaron band dispersion. Particular emphasis is laid on the different physics occurring in the adiabatic and anti-adiabatic regimes, respectively. Comparison is made with a cluster approach exploiting exact numerical results on small systems to yield an approximation for the thermodynamic limit. This method, similar to cluster perturbation theory, confirms the analytical findings, and yields accurate results also in the intermediate-coupling regime.

arXiv:cond-mat/0604040•Journal of Physics Condensed Matter•Jul 21, 2006•20 citations

Spectral function of electron-phonon models by cluster perturbation theory

Martin Hohenadler, Markus Aichhorn, Wolfgang von der Linden

Cluster perturbation theory in combination with the Lanczos method is used to compute the one-electron spectral function of the Holstein polaron in one and two dimensions. It is shown that the method allows reliable calculations using relatively small clusters, and at the same time significantly reduces finite-size effects. Results are compared with exact data and the relation to existing work is discussed. We also use a strong-coupling perturbation theory---equivalent to the Hubbard I approximation---to calculate the spectral function of the quarter-filled Holstein model of spinless fermions, starting from the exact atomic-limit Green function. The results agree well with previous calculations within the many-body coherent potential approximation.

arXiv:cond-mat/0306740•Physical review. B, Condensed matter•Nov 19, 2003•56 citations

Phonon spectral function of Holstein polaron: Investigation of many-body effects with self-energy and vertex correction

Lawrence Rai, Sudhakar Pandey

We study the impact of the many-body effects on the phonon spectral function of Holstein polaron in one-dimension in the antiadiabatic regime by incorporating the contributions from the electron self-energy and vertex corrections within a weak-coupling approach that respects the charge-conserving Ward identity. We find that while the polaronic spectral weight is suppressed due to contribution from the electron self-energy, on the other hand, the same is enhanced due to contribution from the vertex corrections. While strength of both the contributions increases with increasing the wave vector ($\q$) of phonons, they nearly cancel each other for the small-$\q$ modes so that the polaronic spectral weight is weakly affected due to the many-body effects. For the large-$\q$ modes near the zone boundary, the net many-body correction is dominated by the contribution of the electron self-energy which increases faster in comparison to that of the vertex corrections with increasing the wave vector thereby resulting in a significant suppression of the polaronic spectral weight. We find that while the weak-coupling perturbative approach provides a reliable estimation of the impact of the many-body effects deep inside the antiadibatic regime, the renormalization of quasiparticle spectrum must be taken into account for an accurate estimation when the phonon energy approaches the electronic bandwidth.

arXiv:2607.02136•Jul 2, 2026•0 citations

Spectral properties of Holstein and breathing polarons

Cyrill Slezak, Alexandru Macridin, G. A. Sawatzky +2 more

We calculate the spectral properties of the one-dimensional Holstein and breathing polarons using the self-consistent Born approximation. The Holstein model electron-phonon coupling is momentum independent while the breathing coupling increases monotonically with the phonon momentum. We find that for a linear or tight binding electron dispersion: (i) for the same value of the dimensionless coupling the quasiparticle renormalization at small momentum in the breathing polaron is much smaller, (ii) the quasiparticle renormalization at small momentum in the breathing polaron increases with phonon frequency unlike in the Holstein model where it decreases, and (iii) in the Holstein model the quasiparticle dispersion displays a kink and a small gap at an excitation energy equal to the phonon frequency ${\ensuremath{\omega}}_{0}$ while in the breathing model it displays two gaps, one at excitation energy ${\ensuremath{\omega}}_{0}$ and another one at $2{\ensuremath{\omega}}_{0}$. These differences have two reasons: first, the momentum of the relevant scattered phonons increases with increasing polaron momentum and second, the breathing bare coupling is an increasing function of the phonon momentum. These result in an effective electron-phonon coupling for the breathing model which is an increasing function of the total polaron momentum, such that the small momentum polaron is in the weak coupling regime while the large momentum one is in the strong coupling regime. However, the first reason does not hold if the free electron dispersion has low energy states separated by large momentum, as in a higher dimensional system, for example, in this situation the difference between the two models becomes less significant.

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Spectral functions of the spinless Holstein model

Jan Loos, Martin Hohenadler, Holger Fehske

An analytical approach to the one-dimensional spinless Holstein model is proposed, which is valid at finite charge-carrier concentrations. Spectral functions of charge carriers are computed on the basis of self-energy calculations. A generalization of the Lang–Firsov canonical transformation method is shown to provide an interpolation scheme between the extreme weak-coupling and strong-coupling cases. The transformation depends on a variationally determined parameter that characterizes the charge distribution across the polaron volume. The relation between the spectral functions of the polaron and electron, the latter corresponding to the photoemission spectrum, is derived. Particular attention is paid to the distinction between the coherent and incoherent parts of the spectra, and their evolution as a function of band filling and model parameters. Results are discussed and compared with recent numerical calculations for the many-polaron problem.

arXiv:cond-mat/0508712•Journal of Physics Condensed Matter•Feb 10, 2006•20 citations

Optical conductivity of polaronic charge carriers

Jan Loos, Martin Hohenadler, Andreas Alvermann +1 more

The optical conductivity of charge carriers coupled to quantum phonons is studied in the framework of the one-dimensional spinless Holstein model. For one electron, variational diagonalization yields exact results in the thermodynamic limit, whereas at finite carrier density analytical approximations based on previous work on single-particle spectral functions are obtained. Particular emphasis is put on deviations from weak-coupling, small-polaron or one-electron theories occurring at intermediate coupling and/or finite carrier density. The analytical results are in surprisingly good agreement with exact data, and exhibit the characteristic polaronic excitations observed in experiments on manganites.

arXiv:cond-mat/0703611•Journal of Physics Condensed Matter•May 17, 2007•13 citations
The phonon spectral function of the one-dimensional Holstein model is obtained within weak and strong-coupling approximations based on analytical self-energy calculations.The characteristic excitations found in the limit of small charge-carrier density are related to the known (electronic) spectral properties of Holstein polarons such as the polaron band dispersion.Particular emphasis is laid on the different physics occurring in the adiabatic and antiadiabatic regimes, respectively.Comparison is made with a cluster approach exploiting exact numerical results on small systems to yield an approximation for the thermodynamic limit.This method, similar to cluster perturbation theory, confirms the analytical findings, and yields accurate results also in the intermediate-coupling regime.
The phonon spectral function of the one-dimensional Holstein model is obtained within weak and strong-coupling approximations based on analytical self-energy calculations. The characteristic excitations found in the limit of small charge-carrier density are related to the known (electronic) spectral properties of Holstein polarons such as the polaron band dispersion. Particular emphasis is laid on the different physics occurring in the adiabatic and anti-adiabatic regimes, respectively. Comparison is made with a cluster approach exploiting exact numerical results on small systems to yield an approximation for the thermodynamic limit. This method, similar to cluster perturbation theory, confirms the analytical findings, and yields accurate results also in the intermediate-coupling regime.
Cluster perturbation theory in combination with the Lanczos method is used to compute the one-electron spectral function of the Holstein polaron in one and two dimensions. It is shown that the method allows reliable calculations using relatively small clusters, and at the same time significantly reduces finite-size effects. Results are compared with exact data and the relation to existing work is discussed. We also use a strong-coupling perturbation theory---equivalent to the Hubbard I approximation---to calculate the spectral function of the quarter-filled Holstein model of spinless fermions, starting from the exact atomic-limit Green function. The results agree well with previous calculations within the many-body coherent potential approximation.
We study the impact of the many-body effects on the phonon spectral function of Holstein polaron in one-dimension in the antiadiabatic regime by incorporating the contributions from the electron self-energy and vertex corrections within a weak-coupling approach that respects the charge-conserving Ward identity. We find that while the polaronic spectral weight is suppressed due to contribution from the electron self-energy, on the other hand, the same is enhanced due to contribution from the vertex corrections. While strength of both the contributions increases with increasing the wave vector ($\q$) of phonons, they nearly cancel each other for the small-$\q$ modes so that the polaronic spectral weight is weakly affected due to the many-body effects. For the large-$\q$ modes near the zone boundary, the net many-body correction is dominated by the contribution of the electron self-energy which increases faster in comparison to that of the vertex corrections with increasing the wave vector thereby resulting in a significant suppression of the polaronic spectral weight. We find that while the weak-coupling perturbative approach provides a reliable estimation of the impact of the many-body effects deep inside the antiadibatic regime, the renormalization of quasiparticle spectrum must be taken into account for an accurate estimation when the phonon energy approaches the electronic bandwidth.
We calculate the spectral properties of the one-dimensional Holstein and breathing polarons using the self-consistent Born approximation. The Holstein model electron-phonon coupling is momentum independent while the breathing coupling increases monotonically with the phonon momentum. We find that for a linear or tight binding electron dispersion: (i) for the same value of the dimensionless coupling the quasiparticle renormalization at small momentum in the breathing polaron is much smaller, (ii) the quasiparticle renormalization at small momentum in the breathing polaron increases with phonon frequency unlike in the Holstein model where it decreases, and (iii) in the Holstein model the quasiparticle dispersion displays a kink and a small gap at an excitation energy equal to the phonon frequency ${\ensuremath{\omega}}_{0}$ while in the breathing model it displays two gaps, one at excitation energy ${\ensuremath{\omega}}_{0}$ and another one at $2{\ensuremath{\omega}}_{0}$. These differences have two reasons: first, the momentum of the relevant scattered phonons increases with increasing polaron momentum and second, the breathing bare coupling is an increasing function of the phonon momentum. These result in an effective electron-phonon coupling for the breathing model which is an increasing function of the total polaron momentum, such that the small momentum polaron is in the weak coupling regime while the large momentum one is in the strong coupling regime. However, the first reason does not hold if the free electron dispersion has low energy states separated by large momentum, as in a higher dimensional system, for example, in this situation the difference between the two models becomes less significant.
An analytical approach to the one-dimensional spinless Holstein model is proposed, which is valid at finite charge-carrier concentrations. Spectral functions of charge carriers are computed on the basis of self-energy calculations. A generalization of the Lang–Firsov canonical transformation method is shown to provide an interpolation scheme between the extreme weak-coupling and strong-coupling cases. The transformation depends on a variationally determined parameter that characterizes the charge distribution across the polaron volume. The relation between the spectral functions of the polaron and electron, the latter corresponding to the photoemission spectrum, is derived. Particular attention is paid to the distinction between the coherent and incoherent parts of the spectra, and their evolution as a function of band filling and model parameters. Results are discussed and compared with recent numerical calculations for the many-polaron problem.
The optical conductivity of charge carriers coupled to quantum phonons is studied in the framework of the one-dimensional spinless Holstein model. For one electron, variational diagonalization yields exact results in the thermodynamic limit, whereas at finite carrier density analytical approximations based on previous work on single-particle spectral functions are obtained. Particular emphasis is put on deviations from weak-coupling, small-polaron or one-electron theories occurring at intermediate coupling and/or finite carrier density. The analytical results are in surprisingly good agreement with exact data, and exhibit the characteristic polaronic excitations observed in experiments on manganites.