论文标题
$α-T_3 $晶格中的几何淬火和动态量子相变
Geometrical quench and dynamical quantum phase transition in the $α-T_3$ lattice
论文作者
论文摘要
我们研究了量子淬灭和Loschmidt Echo在二维三个频段$α-T_3 $模型中，这是骰子晶格的亲密后代。通过向中央部位添加化学电位，可以通过sublattices之间的跳跃积分的比率来调节不同山谷中带的浆果曲率的积分。通过研究一个和两个填充的频段，我们发现动态量子相变（DQPT），即回归幅度速率函数中的非分析时间行为，对于一定范围的参数发生，与频带填充无关。通过关注模型的有效低能描述，我们发现DQPT不仅发生在速率函数的时间导数中，这在二维模型中是一个常见的特征，而且在速率函数本身中。此功能与淬火过程中系统拓扑特性的变化无关，而是遵循所有动量的种群反演。这伴随着在Pancharatnam几何阶段的时光空间中的动态涡流的出现。涡流的位置形成了无限的涡旋梯子，即宏观相结构，这使我们能够识别由DQPT分离的动力相。
We investigate quantum quenches and the Loschmidt echo in the two dimensional, three band $α-T_3$ model, a close descendant of the dice lattice. By adding a chemical potential to the central site, the integral of the Berry curvature of the bands in different valleys is continously tunable by the ratio of the hopping integrals between the sublattices. By investigating one and two filled bands, we find that dynamical quantum phase transition (DQPT), i.e. nonanalytical temporal behaviour in the rate function of the return amplitude, occurs for a certain range of parameters, independent of the band filling. By focusing on the effective low energy description of the model, we find that DQPTs happen not only in the time derivative of the rate function, which is a common feature in two dimensional models, but in the rate function itself. This feature is not related to the change of topological properties of the system during the quench, but rather follows from population inversion for all momenta. This is accompanied by the appearance of dynamical vortices in the time-momentum space of the Pancharatnam geometric phase. The positions of the vortices form an infinite vortex ladder, i.e. a macroscopic phase structure, which allows us to identify the dynamical phases that are separated by the DQPT.
