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Physica Scripta

The One-Dimensional Electron-Phonon System with Forward Scattering Interaction

Ioan Bâldea

Published Jun 1, 1985• 1 citation
Publisher

Abstract

A Ward identity is derived for the one-dimensional system with both electron-electron and electron-phonon forward scattering interactions. This identity is used to solve exactly the Dyson equations of the generalized effective interaction, phonon and electron Green functions for both T = 0 and T ≠ 0. The absence of both the quasi-fermion excitations and the jump in electron momentum distribution at the Fermi "surface" points out the failure of the Landau Fermi liquid theory for this system. The long-wavelength dielectric response function and the thermodynamic potential are also computed exactly.

DOI
10.1088/0031-8949/31/6/024

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The momentum distribution function of a one-dimensional interacting many electron-phonon system is calculated analytically within the framework of the Luttinger model. We have shown that, even a small electron-electron interaction destroys the fermi surface and in the presence of the electron-phonon interaction the residual fermi surface vanishes completely and the function becomes a continuous function of the wave vector as we increase the coupling strength. It shows that in one dimension, the Fermi liquid theory breaks down completely, if we include the electron-phonon interactions along with the electron-electron interaction.
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We consider a specific generalization to spatial dimensions d greater than one of a formalism, based upon conservation laws and the associated ward identities, that exactly solves the one-dimensional Luttinger model, and expose its inadequacies for d > 1. We conclude that findings arrived at through application of this generalized formalism concerning systems of fermions with strong forward scattering, in particular that d = 1 would be the cross-over dimension from Luttinger- to Fermi-liquid state, are open to question.