The Houston states (Krieger and Iafrate in Phys Rev B 33: 5494 1986), which are instantaneous eigenstates of the time-dependent Hamiltonian, are known as an appropriate basis function to observe the role of each band in high-order harmonic generation (HHG) in solids. However, due to the sharp blow-up of the transition matrix elements between the Houston states (Wu et al. in Phys Rev A 91: 043839 2015), the Houston state treatment is known to be highly numerically unstable if more than two conduction bands are included. We develop a smooth variable discretization (SVD) method with Houston states by exploiting the fact that the wave function varies smoothly in time to solve the time-dependent Schrödinger equation (TDSE) for a solid exposed to a strong laser field. We demonstrate that the SVD method with the Houston states is numerically stable and can avoid the blow-up. Using the SVD method with the Houston states, we investigate the role of each band for the multiple plateau structure in HHG, and we find that strongly coupled bands should be treated as a whole and that the traditional classification of the currents into interband and intraband currents is not a suitable way to understand the plateaus in the HHG spectrum.

休斯顿状态（Krieger和Iafrate在Phys Rev B 33：5494 1986中）是随时间变化的哈密顿量的瞬时本征态，被认为是观察每个频带在高次谐波产生中的作用的适当基函数（HHG）。 ）的固体。但是，由于休斯顿状态之间的过渡矩阵元素急剧爆炸（Wu等人，Phys Rev A 91：043839 2015），因此，如果超过两个导带，则休斯顿状态处理在数值上非常不稳定被包含在内。我们利用波函数随时间平滑变化的事实来求解休斯顿状态下的光滑变量离散化（SVD）方法，以解决暴露于强激光场的固体随时间变化的薛定ding方程（TDSE）的问题。我们证明了具有休斯顿状态的SVD方法在数值上是稳定的，可以避免爆炸。使用具有休斯敦州的SVD方法，我们研究了每个频带对于HHG中多平台结构的作用，并且我们发现强耦合频带应作为一个整体来对待，并且将电流传统划分为带间和带内电流这不是了解HHG频谱平稳期的合适方法。