Breakdown of Migdal–Eliashberg Theory via Catastrophic Vertex Divergence at Low Phonon Frequency

Hague, J. P.; d’Ambrumenil, N.

doi:10.1007/s10909-008-9800-z

Cited by 24 publications

(26 citation statements)

References 33 publications

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“…48,[50][51][52][53][54] As long as g is not close to the critical value g c for the transition to the bipolaronic insulating phase and ω 0 is small compared to the electron bandwidth, it provides a qualitatively good description. 48,53 Since the self-energies of the electrons and phonons involve dressed propagators (as sketched in Fig.…”

Section: B Observablesmentioning

confidence: 99%

“…This type of approximation has also been employed in recent studies of the dynamics of the Holstein model driven by strong laser fields. [34][35][36] The other is the self-consistent Migdal approximation, 48,[50][51][52][53][54] where the dressed phonon propagator is used and thus the phonon dynamics affects the electron self-energy and vice versa. In the following, we call the former approximation the Hartree-Fock (HF) approximation and the latter the Migdal approximation, see Fig.…”

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confidence: 99%

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Interaction quench in the Holstein model: Thermalization crossover from electron- to phonon-dominated relaxation

et al. 2015

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We study the relaxation of the Holstein model after a sudden switch-on of the interaction by means of the nonequilibrium dynamical mean field theory, with the self-consistent Migdal approximation as an impurity solver. We show that there exists a qualitative change in the thermalization dynamics as the interaction is varied in the weak-coupling regime. On the weaker interaction side of this crossover, the phonon oscillations are damped more rapidly than the electron thermalization timescale, as determined from the relaxation of the electron momentum distribution function. On the stronger interaction side, the relaxation of the electrons becomes faster than the phonon damping. In this regime, despite long-lived phonon oscillations, a thermalized momentum distribution is realized temporarily. The origin of the "thermalization crossover" found here is traced back to different behaviors of the electron and phonon self-energies as a function of the electron-phonon coupling. In addition, the importance of the phonon dynamics is demonstrated by comparing the self-consistent Migdal results with those obtained with a simpler Hatree-Fock impurity solver that neglects the phonon self-energy. The latter scheme does not properly describe the evolution and thermalization of isolated electron-phonon systems.

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Section: B Observablesmentioning

confidence: 99%

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confidence: 99%

Interaction quench in the Holstein model: Thermalization crossover from electron- to phonon-dominated relaxation

et al. 2015

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“…[8][9][10][11][12] In the adiabatic limit, Benedetti and Zeyher 8 found a breakdown of Migdal's theorem due to the appearance of additional extremal paths in the action for λ > ∼ 0.4. 7 Capone and Ciuchi 11 found quantitative deviations of self-consistent ME calculations from DMFT already for intermediate coupling strengths and qualitatively different behavior for stronger coupling.…”

Section: 6mentioning

confidence: 99%

“…(6) and (7) for the DMFT calculation. Thus by ME theory we mean the diagrammatic theory, which neglects all vertex corrections to (12), and as such it is compared to the full DMFT results. No further approximation such as assuming a constant density of states or large bandwidth are made.…”

Section: 22mentioning

confidence: 99%

Quantitative reliability study of the Migdal-Eliashberg theory for strong electron-phonon coupling in superconductors

2011

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We reassess the validity of Migdal-Eliashberg (ME) theory for coupled electron-phonon systems for large couplings λ. Although model calculations have found that ME theory breaks down for λ ∼ 0.5, it is routinely applied for λ > 1 to strong coupling superconductors. To resolve this discrepancy it is important to distinguish between bare parameters, used as input in models, and effective parameters, derived from experiments. We show explicitly that ME gives accurate results for the critical temperature and the spectral gap for large effective λ. This provides quantitative theoretical support for the applicability of ME theory to strong coupling conventional superconductors.

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“…In order to solve the effective impurity model, we employ the self-consistent Migdal approximation [23][24][25]35,[43][44][45][46][47], which is justified when the phonon frequency ω 0 is small enough compared to the electron bandwidth [35,[43][44][45]. Here, the electron self-energy (ˆ ) and phonon self-energy ( ) are given bŷ…”

Section: Migdal Approximationmentioning

confidence: 99%

Nonequilibrium steady states and transient dynamics of conventional superconductors under phonon driving

Murakami¹,

Tsuji²,

Eckstein³

et al. 2017

Phys. Rev. B

156

138

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We perform a systematic analysis of the influence of phonon driving on the superconducting Holstein model coupled to heat baths by studying both the transient dynamics and the nonequilibrium steady state (NESS) in the weak and strong electron-phonon coupling regimes. Our study is based on the nonequilibrium dynamical mean-field theory, and for the NESS we present a Floquet formulation adapted to electron-phonon systems. The analysis of the phonon propagator suggests that the effective attractive interaction can be strongly enhanced in a parametric resonant regime because of the Floquet side bands of phonons. While this may be expected to enhance the superconductivity (SC), our fully self-consistent calculations, which include the effects of heating and nonthermal distributions, show that the parametric phonon driving generically results in a suppression or complete melting of the SC order. In the strong coupling regime, the NESS always shows a suppression of the SC gap, the SC order parameter, and the superfluid density as a result of the driving, and this tendency is most prominent at the parametric resonance. Using the real-time nonequilibrium DMFT formalism, we also study the dynamics towards the NESS, which shows that the heating effect dominates the transient dynamics, and SC is weakened by the external driving, in particular at the parametric resonance. In the weak coupling regime, we find that the SC fluctuations above the transition temperature are generally weakened under the driving. The strongest suppression occurs again around the parametric resonances because of the efficient energy absorption.

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Breakdown of Migdal–Eliashberg Theory via Catastrophic Vertex Divergence at Low Phonon Frequency

Cited by 24 publications

References 33 publications

Interaction quench in the Holstein model: Thermalization crossover from electron- to phonon-dominated relaxation

Interaction quench in the Holstein model: Thermalization crossover from electron- to phonon-dominated relaxation

Quantitative reliability study of the Migdal-Eliashberg theory for strong electron-phonon coupling in superconductors

Nonequilibrium steady states and transient dynamics of conventional superconductors under phonon driving

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