Operator Valued Flow Equation Approach to the Bosonic Lattice Polaron: Dispersion Renormalization Beyond the Fr\"ohlich Paradigm

TL;DR

This paper introduces an operator valued flow equation method to analyze the ground state and dispersion of a lattice Bose polaron, revealing significant effects of two-phonon processes and predicting a novel bound state absent in simpler models.

Contribution

The study extends flow equation techniques to include two-phonon scattering, providing new insights into polaron dispersion and bound state formation beyond Fr"ohlich models.

Findings

Two-phonon scattering significantly alters polaron dispersion.

A polaronic bound state can emerge due to two-phonon processes.

Results differ from traditional single-phonon models.

Abstract

We consider the ground state properties of a lattice Bose polaron, a quasiparticle arising from the interaction between an impurity confined to an optical lattice and a surrounding homogeneous Bose-Einstein condensate hosting phononic modes. We present an extension of Wegner's and Wilson's flow equation approach, the operator valued flow equation approach, which allows us to calculate the renormalized dispersion of the polaron and assess the role of two-phonon scattering processes on the dispersion. The results obtained in this way are compared to a variational mean-field approach. We find that in certain impurity phonon interaction regimes the shape of the dispersion is significantly altered by the inclusion of two-phonon scattering events as opposed to only single-phonon scattering events. Moreover, our results predict that a polaronic bound state may emerge, which is not present in Fr\"ohlich-type models that only consider single-phonon scattering events.