Quantum groups as hidden symmetries of quantum impurities Yakaboylu, Enderalp ; https://orcid.org/0000-0001-5973-0874 Shkolnikov, Mikhail ; https://orcid.org/0000-0002-4310-178X Lemeshko, Mikhail ; https://orcid.org/0000-0002-6990-7802 We present an approach to interacting quantum many-body systems based on the notion of quantum groups, also known as q-deformed Lie algebras. In particular, we show that, if the symmetry of a free quantum particle corresponds to a Lie group G, in the presence of a many-body environment this particle can be described by a deformed group, Gq. Crucially, the single deformation parameter, q, contains all the information about the many-particle interactions in the system. We exemplify our approach by considering a quantum rotor interacting with a bath of bosons, and demonstrate that extracting the value of q from closed-form solutions in the perturbative regime allows one to predict the behavior of the system for arbitrary values of the impurity-bath coupling strength, in good agreement with nonperturbative calculations. Furthermore, the value of the deformation parameter allows one to predict at which coupling strengths rotor-bath interactions result in a formation of a stable quasiparticle. The approach based on quantum groups does not only allow for a drastic simplification of impurity problems, but also provides valuable insights into hidden symmetries of interacting many-particle systems. American Physical Society 2018 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/5794 Yakaboylu E, Shkolnikov M, Lemeshko M. Quantum groups as hidden symmetries of quantum impurities. <i>Physical Review Letters</i>. 2018;121(25). doi:<a href="https://doi.org/10.1103/PhysRevLett.121.255302">10.1103/PhysRevLett.121.255302</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevLett.121.255302 info:eu-repo/semantics/altIdentifier/issn/00319007 info:eu-repo/semantics/altIdentifier/wos/000454178600009 info:eu-repo/semantics/altIdentifier/arxiv/1809.00222 info:eu-repo/semantics/openAccess