First-principles ultrafast phonon dynamics by solving the real-time Boltzmann transport equation with adaptive multirate time stepping*

Ultrafast lattice dynamics in materials can be accessed with pump-probe spectroscopies and used to prepare novel nonequilibrium quantum phases. Therefore, quantitative modeling of ultrafast lattice dynamics would advance nonequilibrium physics. Electron dynamics can be modeled by the electron real-time Boltzmann transport equation (rt-BTE) with first-principles electron-phonon (e-ph) collisions using an efficient parallel algorithm [1]. Yet, solving the lattice (phonon) rt-BTE with e-ph and phonon-phonon (ph-ph) collisions [2] remains challenging due to the different timescales of e-ph and ph-ph interactions. In this work, we interface the PERTURBO code [1] with the SUNDIALS library [3] to efficiently advance coupled electron and phonon rt-BTEs in time. We demonstrate a significant speed-up using adaptive step size and multirate infinitesimal (MRI) methods from SUNDIALS that enable utilizing different time step sizes for fast-evolving, cheap e-ph interaction and the slow, expensive ph-ph interaction. These advances allow us to model ultrafast lattice dynamics in real materials with moderate computational cost. Application to graphene and silicon will demonstrate the capabilities of this novel first-principles tool, which expands the scope of nonequilibrium first-principles calculations.

[1] J.-J. Zhou, et al. Comput. Phys. Commun. 264,107970 (2021)

[2] X. Tong, M. Bernardi, Phys. Rev. Research, 3 (2021)

[3] D. R. Reynolds, et al. ACM Trans. on Math. Software, 49(2), pp. 1-26 (2023)