Sorting and assigning phonon branches (e.g., longitudinal acoustic) of phonon modes is important for characterizing the phonon bands of a crystal and the determination of phonon properties such as the Grneisan parameter and group velocity. To do this, the phonon band indices (including the longitudinal and transverse acoustic) have to be assigned correctly to all phonon modes across a path or paths in the Brillouin zone. As our solution to this challenging problem, we propose a computationally efficient and robust two-stage hybrid method that combines two approaches with their own merits. The first is the perturbative approach in which we connect the modes using degenerate perturbation theory. In the second approach, we use numerical fitting based on least-squares fits to circumvent local connectivity errors at or near exact degenerate modes. The method can be easily generalized to other condensed matter problems involving Hermitian matrix operators such as electronic bands in tight-binding Hamiltonians or in a standard density-functional calculation, and photonic bands in photonic crystals.

对声子模式的声子分支（例如，纵向声波）进行分类和分配对于表征晶体的声子带以及确定声子性质（如Grneisan参数和群速度）很重要。为此，必须在布里渊区中的一条路径或多条路径上，将声子能带指数（包括纵向和横向声波）正确分配给所有声子模式。作为解决这一难题的方法，我们提出了一种计算效率高且鲁棒的两阶段混合方法，该方法结合了两种方法的优点。第一种是微扰方法，其中我们使用简并扰动理论连接模式。在第二种方法中，我们使用基于最小二乘拟合的数值拟合来规避处于或接近精确简并模式的局部连接错误。