Electron and phonon dispersions of the two-dimensional Holstein model: effects ofvertex and non-local corrections

Abstract

I apply the newly developed dynamical cluster approximation (DCA) to thecalculation of the electron and phonon dispersions in the two-dimensional Holsteinmodel. In contrast to previous work, the DCA enables the effects of spatialfluctuations (non-local corrections) to be examined. Approximations neglectingand incorporating lowest-order vertex corrections are investigated. I calculate thephonon density of states, the renormalized phonon dispersion, the electrondispersion and electron spectral functions. I demonstrate how vertex correctionsstabilize the solution, stopping a catastrophic softening of the (π, π) phononmode. A kink in the electron dispersion is found in the normal state along the (ζ, ζ)symmetry direction in both the vertex- and non-vertex-corrected theories for low phononfrequencies, corresponding directly to the renormalized phonon frequency at the (π, 0)point. This kink is accompanied by a sudden drop in the quasi-particle lifetime.Vertex and non-local corrections enhance the effects at large bare phononfrequencies.