论文标题
部分可观测时空混沌系统的无模型预测
Realization of the topological Hopf term in two-dimensional lattice models
论文作者
论文摘要
众所周知，二维自旋系统可以通过与无质量的狄拉克费米子耦合，其能量光谱具有单个锥体。但是，由于低能频谱中的费米亚倍增，意识到凝结物理学的HOPF术语是具有挑战性的。在这项工作中，我们提出了一个场景，以实现晶格模型中的HOPF术语。中心目的是调整旋转与狄拉克费米子之间的耦合，以使两个锥体贡献的拓扑术语不会相互抵消。为此，我们考虑$ p_x $和$ p_y $ orbitals在蜂窝晶状体上的dirac费米子，因此总共有四个频段。通过利用轨道自由度，在集成了Dirac Fermions后，为旋转系统成功生成了$θ=2π$ hopf项。如果费米子具有较小的差距$ m_0 $，或者考虑了自旋轨道耦合，则不再量化$θ$，但可能会流向重新规范化的$2π$的多个。讨论了具有HOPF术语的旋转系统的基态和物理响应。
It is known that a two-dimensional spin system can acquire a topological Hopf term by coupling to massless Dirac fermions whose energy spectrum has a single cone. But it is challenging to realize the Hopf term in condensed matter physics due to the fermion-doubling in the low-energy spectrum. In this work we propose a scenario to realize the Hopf term in lattice models. The central aim is tuning the coupling between the spins and the Dirac fermions such that the topological terms contributed by the two cones do not cancel each other. To this end, we consider $p_x$ and $p_y$ orbitals for the Dirac fermions on the honeycomb lattice such that there are totally four bands. By utilizing the orbital degrees of freedom, a $θ=2π$ Hopf term is successfully generated for the spin system after integrating out the Dirac fermions. If the fermions have a small gap $m_0$ or if the spin-orbit coupling is considered, then $θ$ is no longer quantized, but it may flow to multiple of $2π$ under renormalization. The ground state and the physical response of a spin system having the Hopf term are discussed.
