# Adiabatic corrections for velocity-gauge simulations of electron dynamics in periodic potentials

## TL;DR

This paper introduces analytical corrections for velocity-gauge simulations that reduce computational complexity and resolve divergence issues in modeling electron dynamics in crystalline solids.

## Contribution

The authors derive band-energy-dependent corrections that improve convergence and eliminate divergences in velocity-gauge electron dynamics simulations.

## Key findings

- Significantly reduces the number of energy bands needed.
- Overcomes divergence problems in susceptibility calculations.
- Enhances accuracy and efficiency of light-matter interaction modeling.

## Abstract

We show how to significantly reduce the number of energy bands required to model the interaction of light with crystalline solids in the velocity gauge. We achieve this by deriving analytical corrections to the electric current density. These corrections depend only on band energies, the matrix elements of the momentum operator, and the macroscopic vector potential. Thus, the corrections can be evaluated independently from modeling the interaction with light. In addition to improving the convergence of velocity-gauge calculations, our analytical approach overcomes the long-standing problem of divergences in expressions for linear and nonlinear susceptibilities.