短程相互作用对准粒子相对论动力学的影响

通过调节短程相互作用,在Su-Schrieffer-Heeger(SSH)模型中实现了Dirac点的移动与融合.该过程对应于一种由半金属相到能带绝缘相的拓扑相变(即Lifshitz相变).通过解析和数值研究的方法,对该相变过程中系统准粒子的相对论动力学特性进行了研究.结果表明:在短程相互作用很弱的情况下(即Dirac点融合前),系统展现出相对论动力学特征;然而,随着短程相互作用的增强,Dirac点会发生融合相变.此后,系统则表现为非相对论动力学特征.因此,相变过程是由相对论到非相对论动力学转变的过程.进一步通过数值模拟得到了融合前(相对论)后(非相对论)粒子的密度分布随时间演化的图像.在相变前,单色Dirac准粒子发生劈裂,而双色Dirac准粒子产生定向漂移现象.在相变后,无论初态如何改变,系统始终无组分劈裂现象出现.最后,展示了不同相互作用下准粒子的质心运动曲线(世界线).

The Influence of Short-Range Interaction on the Relativistic Dynamics of Quasi-Particles

The movement and merging of Dirac points were realized in the Su-Schrieffer-Heeger (SSH) model by adjusting short-range interaction. This process corresponded to a topological phase transition from a semi-metallic to a band insulating phase, known as Lifshitz phase transition. The dynamical properties of relativistic quasi-particles in this process were investigated with the analytical and numerical methods. The system exhibited relativistic dynamics under the condition of weak short-range interaction (i.e., before the merging of Dirac points). However, with the increase of the short-range interaction, the merging of Dirac points occurred. After that the system showed non-relativistic dynamics. Therefore, the phase transition was also a transition from relativistic to nonrelativistic dynamics. Furthermore, through numerical simulation, a vivid evolution of quasi-particles' density distribution versus time was presented before (relativistic) and after (non-relativistic) the merging transition. The results reveal that before the phase transition the monochromatic Dirac quasi-particles split while the bi-chromatic Dirac quasi-particles directionally drift. Furthermore, after the phase transition, no matter how the initial state changes, no component splitting occurs in the system. Finally, the centroid motion curves (worldlines) of quasi-particles under different interaction conditions are provided.