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.
Physical Review Letters
Yakaboylu E, Shkolnikov M, Lemeshko M. Quantum groups as hidden symmetries of quantum impurities. Physical Review Letters. 2018;121(25). doi:10.1103/PhysRevLett.121.255302
Yakaboylu, E., Shkolnikov, M., & Lemeshko, M. (2018). Quantum groups as hidden symmetries of quantum impurities. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.121.255302
Yakaboylu, Enderalp, Mikhail Shkolnikov, and Mikhail Lemeshko. “Quantum Groups as Hidden Symmetries of Quantum Impurities.” Physical Review Letters. American Physical Society, 2018. https://doi.org/10.1103/PhysRevLett.121.255302.
E. Yakaboylu, M. Shkolnikov, and M. Lemeshko, “Quantum groups as hidden symmetries of quantum impurities,” Physical Review Letters, 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, Enderalp, et al. “Quantum Groups as Hidden Symmetries of Quantum Impurities.” Physical Review Letters, vol. 121, no. 25, 255302, American Physical Society, 2018, doi:10.1103/PhysRevLett.121.255302.