A theoretical treatment for the orbital response of an infinite, periodic system to a static, homogeneous, magnetic field is presented. It is assumed that the system of interest has an energy gap separating occupied and unoccupied orbitals and a zero Chern number. In contrast to earlier studies, we do not utilize a perturbation expansion, although we do assume the field is sufficiently weak that the occurrence of Landau levels can be ignored. The theory is developed by analyzing results for large, finite systems and also by comparing with the analogous treatment of an electrostatic field. The resulting many-electron Hamilton operator is forced to be hermitian, but hermiticity is not preserved, in general, for the subsequently derived single-particle operators that determine the electronic orbitals. However, we demonstrate that when focusing on the canonical solutions to the single-particle equations, hermiticity is preserved. The issue of gauge-origin dependence of approximate solutions is addressed. Our approach is compared with several previously proposed treatments, whereby limitations in some of the latter are identified.

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规则扩展和无限周期系统对磁场的电子轨道响应。一，静态案例的理论基础

提出了一种对无限周期系统对静态，均匀磁场的轨道响应的理论方法。假设感兴趣的系统具有一个能隙，该能隙将占用和未占用的轨道分隔开，零切恩数。与早期的研究相反，我们没有使用扰动扩展，尽管我们确实假设场足够弱，可以忽略Landau水平的发生。该理论是通过分析大型有限系统的结果并与静电场的类似处理方法进行比较而发展起来的。最终得到的多电子哈密顿算子被迫成为厄米特数，但对于随后确定电子轨道的单粒子算子，通常不保留遗传率。然而，我们证明，当专注于单粒子方程的规范解时，可以保留遗传性。解决了近似解的规范源依赖问题。我们的方法与几种先前提出的治疗方法进行了比较，从而确定了后者的局限性。