论文标题
没有本本征的计算可观察到的物品：Bloch Hamiltonians的申请
Computing observables without eigenstates: applications to Bloch Hamiltonians
论文作者
论文摘要
计算哈密顿量的可观察结果需要在本征态的基础上取矩阵元素。由于本征态仅定义为依赖于哈密顿参数的任意阶段，因此通常难以简化可观察到的分析表达式。在这项工作中，我们展示了如何使用su（n）代数的属性来表达所有可观察到的小时尺寸n所有可观察到的物品，我们如何得出n = 2,3,4的显式表达式。然后，我们提出了多种应用晶体中Bloch电子情况的应用，包括计算浆果曲率，量子公制和轨道矩，以及在非线性响应中可观察到的更复杂的，即线性光钙化效应（LPGE）。作为一个物理示例，我们考虑具有淋巴结变性的多型汉密尔顿人，首先显示这些可观察物之间的约束在从两个波段到三波段模型时如何放松，其次是二次分散如何在小频率下导致恒定的LPGE。
Calculating the observables of a Hamiltonian requires taking matrix elements of operators in the eigenstate basis. Since eigenstates are only defined up to arbitrary phases that depend on Hamiltonian parameters, analytical expressions for observables are often difficult to simplify. In this work, we show how for small Hilbert space dimension N all observables can be expressed in terms of the Hamiltonian and its eigenvalues using the properties of the SU(N) algebra, and we derive explicit expressions for N=2,3,4. Then we present multiple applications specializing to the case of Bloch electrons in crystals, including the computation of Berry curvature, quantum metric and orbital moment, as well as a more complex observable in non-linear response, the linear photogalvanic effect (LPGE). As a physical example we consider multiband Hamiltonians with nodal degeneracies to show first how constraints between these observables are relaxed when going from two to three-band models, and second how quadratic dispersion can lead to constant LPGE at small frequencies.
