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Operator-valued-flow-equation approach to the bosonic lattice polaron: Dispersion renormalization beyond the Fröhlich paradigm

Jan-Philipp Christ, Pit Bermes, and Fabian Grusdt

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Phys. Rev. A 112, 033317 – Published 15 September, 2025

DOI: https://doi.org/10.1103/pcsy-czjp

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, which will allow us to demonstrate that the flow equations behave correctly at weak coupling. 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 Fröhlich-type models that only consider single-phonon scattering events.

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Phys. Rev. A 112, 033317– Published 15 September, 2025
  • Received 10 December 2024
  • Revised 8 April 2025
  • Accepted 30 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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