晶格几何相关量与独立量的对比：Berry曲率、能隙和动力学的分支
Contrasting lattice geometry dependent versus independent quantities: ramifications for Berry curvature, energy gaps, and dynamics
摘要：
在周期晶格势中的电子、光子或冷原子动力学的紧束缚描述中，粒子运动是根据晶格中物理轨道对应的离散点的抽象网络上的跳跃幅度和势来描述的。轨道的物理属性，包括它们在三维空间中的位置，是独立的信息。在本文中，我们确定了一个概念的几何无关性：任何物理量或观察，只依赖于紧束缚参数（而不是在明确的信息有关的轨道几何）被称为“几何无关。“能带结构本身，例如二维系统中能带的陈数，是与几何无关的，而布洛赫带的贝里曲率是与几何相关的。仔细识别几何相关量与独立量可以用作约束各种结果的新原则。通过将几何无关性的概念推广到某些相互作用系统，其中多体能隙明显是几何无关的，我们揭示了分数阶陈氏绝缘体的多体能隙与布里渊区布洛赫带Berry曲率均匀性之间的一种假设关系.我们还探讨了半经典波包动力学的几何依赖性，并使用这一原则来说明如何两种不同类型的霍尔响应测量可能会得到显着不同的结果，由于一个是几何依赖性，而另一个是几何无关的。类似的考虑适用于电子和自旋系统中的反常热霍尔响应。
英文摘要：
In the tight-binding description of electronic, photonic, or cold atomic dynamics in a periodic lattice potential, particle motion is described in terms of hopping amplitudes and potentials on an abstract network of discrete sites corresponding to physical orbitals in the lattice. The physical attributes of the orbitals, including their locations in three-dimensional space, are independent pieces of information. In this paper we identify a notion of geometry-independence: any physical quantity or observable that depends only on the tight-binding parameters (and not on the explicit information about the orbital geometry) is said to be "geometry-independent." The band structure itself, and for example the Chern numbers of the bands in a two-dimensional system, are geometry-independent, while the Bloch-band Berry curvature is geometry-dependent. Careful identification of geometry-dependent versus independent quantities can be used as a novel principle for constraining a variety of results. By extending the notion of geometry-independence to certain classes of interacting systems, where the many-body energy gap is evidently geometry-independent, we shed new light on a hypothesized relation between many-body energy gaps of fractional Chern insulators and the uniformity of Bloch band Berry curvature in the Brillouin zone. We furthermore explore the geometry-dependence of semiclassical wave packet dynamics, and use this principle to show how two different types of Hall response measurements may give markedly different results due to the fact that one is geometry-dependent, while the other is geometry-independent. Similar considerations apply for anomalous thermal Hall response, in both electronic and spin systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
