data of Solid-State High-Harmonic Generation in Different Bases : Convergence and Physical Validity of Truncated Representations

In this work, we investigate the convergence and physical reliability of truncated basis represen-tations in solid-state high-harmonic generation by comparing the stationary Bloch and acceleratedBloch bases. We show that the two representations exhibit intrinsic numerical inequivalence understrong-field driving, leading to distinct carrier dynamics and harmonic emission. The convergencebehaviors of the two bases with respect to the number of retained bands differ qualitatively, with theaccelerated Bloch basis achieving reliable spectral convergence using significantly fewer bands. Byanalyzing the deviation between truncated-band and full-band results, we show that the energeti-cally remote bands affect the harmonic generation through two distinct mechanisms: the populationleakage into higher bands, which mainly leads to intensity renormalization, the modifications of theinterband polarization phase within the truncated subspace, which cause structural distortions ofthe spectrum. These multiband effects can be systematically incorporated into reduced two-banddescriptions through a band-folding correction. Our results provide a physically transparent proce-dure for assessing truncated-basis convergence and offer practical guidance for efficient reduced-basismodeling of strong-field electron dynamics in crystalline solids.本研究通过对比定态布洛赫基（stationary Bloch basis）与加速布洛赫基（accelerated Bloch basis），探究了固态高次谐波产生（solid-state high-harmonic generation）中截断基矢表示的收敛性与物理可靠性。研究表明，在强场驱动（strong-field driving）下，这两种基矢表示存在固有的数值不等价性，进而引发截然不同的载流子动力学与谐波辐射特性。两种基矢随保留能带数目变化的收敛行为存在本质差异：加速布洛赫基仅需极少的保留能带即可实现可靠的光谱收敛（spectral convergence）。通过分析截断能带（truncated-band）与全能带（full-band）结果间的偏差，我们发现高能远程能带（energetically remote bands）通过两种截然不同的机制影响高次谐波产生：其一为向高能带的布居数泄漏（population leakage），该机制主要引发强度重整化（intensity renormalization）；其二为截断子空间（truncated subspace）内带间极化（interband polarization）相位的修正，该机制会导致光谱结构发生畸变（structural distortions of the spectrum）。这类多能带效应（multiband effects）可通过能带折叠修正（band-folding correction）被系统性地整合进简化的双能带描述（reduced two-band descriptions）框架中。本研究结果为截断基矢收敛性的评估提供了物理意义明晰的方法，并为晶体固体（crystalline solids）中强场电子动力学（strong-field electron dynamics）的高效简化基矢建模提供了实用指导。