标题： 量子群作为量子杂质的隐藏对称性 显示英文标题

标题： Quantum groups as hidden symmetries of quantum impurities

摘要： 我们提出了一种基于量子群概念的相互作用量子多体系统的方法，也称为$q$-变形李代数。 特别是，我们表明，如果自由量子粒子的对称性对应于李群$G$，在多体环境存在的情况下，该粒子可以用一个变形群$G_q$来描述。 关键的是，单个变形参数$q$包含了系统中多粒子相互作用的所有信息。 我们通过考虑与玻色子浴相互作用的量子转子来说明我们的方法，并证明在微扰范围内从闭合形式解中提取$q$的值，可以预测杂质-浴耦合强度任意值下的系统行为，与非微扰计算结果一致。 此外，变形参数的值可以用来预测转子-浴相互作用在哪些耦合强度下会导致稳定准粒子的形成。 基于量子群的方法不仅能够大大简化杂质问题，还能为相互作用多粒子系统的隐藏对称性提供有价值的见解。 显示英文摘要

摘要： 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, $G_q$. 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 non-perturbative calculations. Furthermore, the value of the deformation parameter allows 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.