#### Analytical approach to the polaron problem via the q-deformed Lie algebra

Our very own Enderalp Yakaboylu has a new preprint on arXiv about an analytical approach to the polaron through the *q*-deformed Lie algebra!

Abstract:

We present a novel approach to the polaron problem developed on the notion of quantum groups, also known asq-deformed Lie algebras. In this approach, the presence of an impurity in a bath can be depicted as a deformation of the Lie algebra of the bosonic creation and annihilation operators of the bath. In particular, we introduce a simpleq-deformed bosonic Hamiltonian whose truncation on the quartic level in the usual bosonic creation and annihilation operators corresponds to the Fröhlich-Bogoliubov polaron Hamiltonian. By using theq-deformed Lie algebra, the introduced parent Hamiltonian allows us to derive the ground state energy of the Fröhlich-Bogoliubov Hamiltonian analytically for the regime where the Bogoliubov dispersion law takes the phonon-like form

- Enderalp Yakaboylu,
*Analytical approach to the polaron problem via the q-deformed Lie algebra*, [arxiv:2203.14340]

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