Hague, J. P. and d'Ambrumenil, N.. (2008) Breakdown of Migdal-Eliashberg theory via catastrophic vertex divergence at low phonon frequency. Journal of Low Temperature Physics, Vol.151 (No.5-6). pp. 1149-1163. ISSN 0022-2291

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Abstract

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.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Divisions:	Faculty of Science > Physics
Library of Congress Subject Headings (LCSH):	Electron-phonon interactions, Electron-electron interactions
Journal or Publication Title:	Journal of Low Temperature Physics
Publisher:	Springer New York LLC
ISSN:	0022-2291
Date:	June 2008
Volume:	Vol.151
Number:	No.5-6
Number of Pages:	15
Page Range:	pp. 1149-1163
Identification Number:	10.1007/s10909-008-9800-z
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
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URI:	http://wrap.warwick.ac.uk/id/eprint/30265

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