article published yes Enderalp Yakaboylu author 38CB71F6-F248-11E8-B48F-1D18A9856A870000-0001-5973-0874 Mikhail Shkolnikov author 35084A62-F248-11E8-B48F-1D18A9856A870000-0002-4310-178X Mikhail Lemeshko author 37CB05FA-F248-11E8-B48F-1D18A9856A870000-0002-6990-7802 MiLe department International IST Postdoc Fellowship Programme project Quantum rotations in the presence of a many-body environment project 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 Society2018 eng 00319007 1809.00222 00045417860000910.1103/PhysRevLett.121.255302 12125 Yakaboylu, E., Shkolnikov, M., &#38; Lemeshko, M. (2018). Quantum groups as hidden symmetries of quantum impurities. <i>Physical Review Letters</i>. American Physical Society. <a href="https://doi.org/10.1103/PhysRevLett.121.255302">https://doi.org/10.1103/PhysRevLett.121.255302</a> Yakaboylu, Enderalp, et al. “Quantum Groups as Hidden Symmetries of Quantum Impurities.” <i>Physical Review Letters</i>, vol. 121, no. 25, 255302, American Physical Society, 2018, doi:<a href="https://doi.org/10.1103/PhysRevLett.121.255302">10.1103/PhysRevLett.121.255302</a>. Yakaboylu, Enderalp, Mikhail Shkolnikov, and Mikhail Lemeshko. “Quantum Groups as Hidden Symmetries of Quantum Impurities.” <i>Physical Review Letters</i>. American Physical Society, 2018. <a href="https://doi.org/10.1103/PhysRevLett.121.255302">https://doi.org/10.1103/PhysRevLett.121.255302</a>. E. Yakaboylu, M. Shkolnikov, M. Lemeshko, Physical Review Letters 121 (2018). E. Yakaboylu, M. Shkolnikov, and M. Lemeshko, “Quantum groups as hidden symmetries of quantum impurities,” <i>Physical Review Letters</i>, vol. 121, no. 25. American Physical Society, 2018. Yakaboylu E, Shkolnikov M, Lemeshko M. 2018. Quantum groups as hidden symmetries of quantum impurities. Physical Review Letters. 121(25), 255302. 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> 57942019-01-06T22:59:12Z2025-04-15T06:50:24Z