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Annals of Physics

Polaron mobility obtained by a variational approach for lattice Fröhlich models

Milan Kornjača, Nenad Vukmirović

Published Feb 23, 2018• 7 citations
Publisher
DOI
10.1016/j.aop.2018.01.014

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Extending the Fr\"ohlich polaron problem to a discrete ionic lattice we study a polaronic state with a small radius of the wave function but a large size of the lattice distortion. We calculate the energy dispersion and the effective mass of the polaron with the $1/\ensuremath{\lambda}$ perturbation theory and with the exact Monte Carlo method in the nonadiabatic and adiabatic regimes, respectively. The ``small'' Fr\"ohlich polaron is found to be lighter than the small Holstein polaron by 1 or more orders of magnitude.
The Fr\"ohlich model describes the interaction of a mobile impurity with a surrounding bath of phonons which leads to the formation of a quasiparticle, the polaron. In this paper an efficient renormalization group approach is presented which provides a description of Fr\"ohlich polarons in all regimes ranging from weak to strong coupling. The extended renormalization group approach introduced here is capable of predicting ground state properties for arbitrarily small impurity masses. This allows us to obtain the full phase diagram of the Fr\"ohlich Hamiltonian, which we present concretely for the Bogoliubov-Fr\"ohlich model originally introduced to describe ultracold impurities in a Bose-Einstein condensate. For this model, whose regime of validity in ultracold quantum gases is the subject of debate, we benchmark our method by comparison of the ground state energy to recent diagrammatic quantum Monte Carlo calculations.