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.