# Holstein polaron: the effect of multiple phonon modes - Condensed Matter > Superconductivity

Abstract: We generalize the Momentum Average approximations MA$^{0}$ and MA$^{1}$to study the effects of coupling to multiple optical phonons on the propertiesof a Holstein polaron. As for a single phonon mode, these approximations arenumerically very efficient. They become exact for very weak or very strongcouplings, and are highly accurate in the intermediate regimes, {\em e.g.} thespectral weights obey exactly the first six, respectively eight, sum rules. Ourresults show that the effect on ground-state properties is cumulative innature. In particular, if the effective coupling to one mode is much largerthan to the others, this mode effectively determines the GS properties.However, even very weak coupling to a second phonon mode has importantnon-perturbational effects on the higher energy spectrum, in particular on thedispersion and the phonon statistics of the polaron band.

Author: Lucian Covaci, Mona Berciu

Source: https://arxiv.org/