Langevin equation in field theory

Migdal, Alexander; Bershadskii, M. A.; Kozhamkulov, T.A.

doi:10.1007/bf00891882

Cited by 8 publications

(12 citation statements)

References 8 publications

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“…With the development and advances in scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS), IETS has proven invaluable as a tool for identifying and characterizing molecular species within the conduction region. The use of Migdal-Eliashberg theory 28,29 is justified in this case, whereupon the lowest non-vanishing (second) order perturbation in electron-phonon coupling on the Keldysh contour leads to the Born approximation (BA) for electron dynamics. This approach using BA or its selfconsistent (in electron Green function) flavor was used in several theoretical studies 30,31,32,33,34,35,36 .…”

Section: Introductionmentioning

confidence: 99%

Resonant inelastic tunneling in molecular junctions

2006

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Within a phonon-assisted resonance level model we develop a self-consistent procedure for calculating electron transport currents in molecular junctions with intermediate to strong electron-phonon interaction. The scheme takes into account the mutual influence of the electron and phonon subsystems. It is based on the 2 nd order cumulant expansion, used to express the correlation function of the phonon shift generator in terms of the phonon momentum Green function. Equation of motion (EOM) method is used to obtain an approximate analog of the Dyson equation for the electron and phonon Green functions in the case of many-particle operators present in the Hamiltonian. To zero-order it is similar in particular cases (empty or filled bridge level) to approaches proposed earlier. The importance of self-consistency in resonance tunneling situations (partially filled bridge level) is stressed. We confirm, even for strong vibronic coupling, a previous suggestion concerning the absence of phonon sidebands in the current vs. gate voltage plot when the source-drain voltage is small 35 .

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Section: Introductionmentioning

confidence: 99%

Resonant inelastic tunneling in molecular junctions

2006

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“…3 In systems well described by Fermi liquid theory, many of these phenomena are understood within the framework of Migdal and Eliashberg theory, which provides a quantitative account of this physics. 2,4,5 The situation however can be quite different in correlated systems where the role of the e-ph interaction is far less well understood, sometimes even on a qualitative level.…”

Section: Introductionmentioning

confidence: 99%

Determinant quantum Monte Carlo study of the two-dimensional single-band Hubbard-Holstein model

et al. 2013

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We have performed numerical studies of the Hubbard-Holstein model in two dimensions using determinant quantum Monte Carlo (DQMC). Here we present details of the method, emphasizing the treatment of the lattice degrees of freedom, and then study the filling and behavior of the fermion sign as a function of model parameters. We find a region of parameter space with large Holstein coupling where the fermion sign recovers despite large values of the Hubbard interaction. This indicates that studies of correlated polarons at finite carrier concentrations are likely accessible to DQMC simulations. We then restrict ourselves to the half-filled model and examine the evolution of the antiferromagnetic structure factor, other metrics for antiferromagnetic and charge-density-wave order, and energetics of the electronic and lattice degrees of freedom as a function of electron-phonon coupling. From this we find further evidence for a competition between charge-density-wave and antiferromagnetic order at half-filling.

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“…The self-consistent solution of such a self-energy corresponds to the summation of all Feynman diagrams which contain no vertex corrections. In the low (non-zero) phonon-frequency limit, Migdal's analysis indicates a condition, U ω 0 ≪ t 2 , for the neglect of corrections to the vertex function [6].…”

Section: Migdal-eliashberg Theory In the Local Approximationmentioning

confidence: 99%

“…According to an analysis carried out by Migdal, this theory should be valid in the physical regime of electron-phonon problems, where the phonon energy is significantly smaller than the intersite hopping ("Migdal's theorem") [6,7] specifically that the vertex corrections are small when λω 0 /ǫ f ≪ 1 (ω 0 is the phonon frequency and ǫ f the Fermi energy) [34]. On the basis of Migdal's analysis, it is often believed that Migdal-Eliashberg theory is applicable above λ ∼ 1 in the adiabatic limit because of the apparently small size of the vertex corrections, even though in general perturbative approaches break down (i.e.…”

Section: Introductionmentioning

confidence: 99%

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

Hague

d’Ambrumenil

2008

J Low Temp Phys

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We investigate the applicability of Migdal-Eliashberg (ME) theory by revisiting Migdal's analysis within the dynamical mean-field theory framework. First, we compute spectral functions, the quasi-particle weight, the self energy, renormalised phonon frequency and resistivity curves of the half-filled Holstein model. We demonstrate how ME theory has a phase-transition-like instability at intermediate coupling, and how the Engelsberg-Schrieffer (ES) picture is complicated by low-energy excitations from higher order diagrams (demonstrating that ES theory is a very weak coupling approach). Through consideration of the lowest-order vertex correction, we analyse the applicability of ME theory close to this transition. We find a breakdown of the theory in the intermediate coupling adiabatic limit due to a divergence in the vertex function. The region of applicability is mapped out, and it is found that ME theory is only reliable in the weak coupling adiabatic limit, raising questions about the accuracy of recent analyses of cuprate superconductors which do not include vertex corrections.

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Langevin equation in field theory

Cited by 8 publications

References 8 publications

Resonant inelastic tunneling in molecular junctions

Resonant inelastic tunneling in molecular junctions

Determinant quantum Monte Carlo study of the two-dimensional single-band Hubbard-Holstein model

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

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