不同参数下的庞加莱晶体性质比较

Comparison of the properties of Poincaré crystals with different parameters

洛伦兹对称性作为相对论中的基本时空变换,在凝聚态物理中却鲜有应用.为了研究具备洛伦兹对称性的庞加莱晶体理论,构造了不同参数下的庞加莱晶体模型,通过离散庞加莱对称群的幺正表示和多体理论,计算了它们的色散关系、Floquet有效哈密顿量及推迟格林函数.结果发现,在不同参数下,色散关系一致表现出不规则锯齿形状,有效哈密顿量存在着周期性的长程跃迁,传播子表现出回声结晶化现象.该发现加深了对庞加莱晶体性质的理解.

Lorentz symmetry,as a fundamental spacetime transformation in relativity theory,had rarely been applied in condensed matter physics.In order to study the theory of Poincarécrystals with Lorentz symmetry,it was constructed a model of Poincarécrystals with different parameters.It was then proceeded to calculate their dispersion relations,Floquet effective Hamiltonian,and delayed Green′s function by means of the Missing square representation of discrete Poincarésymmetry group and many-body theory.It was found that the dispersion relation consistently exhibited irregular sawtooth shape,the effective Hamiltonian had periodic long-range jumps,and the propagator exhibited echogenic crystallization under different parameters.These findings would deepen the understanding of the properties of Poincarécrystal.