We introduce a practical and accurate strategy to capture light-matter interactions using the Floquet formalism in the velocity gauge in combination with realistic first-principle models of solids. The velocity gauge, defined by the linear coupling to the vector potential, is a standard method to capture the light-matter interaction in solids. However, its use with first-principle models has been limited by the challenging fact that it requires a large number of bands for convergence and its incompatibility with nonlocal pseudopotential plane wave methods. To improve its convergence properties, we explicitly take into account the truncation of Hilbert space in the construction of the Floquet Hamiltonian in the velocity gauge which leads to a series of nested commutators between the position operator and the material Hamiltonian. To avoid the incompatibility with the pseudopotentials and efficiently compute the nested commutators, we base our computations on generalized tight-binding Hamiltonians derived from first-principles through maximally-localized Wannier functions. We exemplify the approach by computing the non-equilibrium optical absorption spectra of laser-dressed trans-polyacetylene chain using realistic electronic structure. We show that, by proceeding in this way, Floquet consideration involving the truncated Hilbert spaces reproduces the full basis calculations with only a few bands and with significantly reduced computation time. The strategy has been implemented in FloqticS, a general code for the Floquet engineering of the optical properties of materials. Overall, this work introduces a useful theoretical tool to realize Floquet engineering of realistic solids in the velocity gauge.

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• Electronic structure
• Light-matter interaction
• Floquet systems
• Bloch-Floquet theorem
• Density functional theory
• Dipole approximation
• Perturbative methods
• Schroedinger equation
• Wannier function methods