First-principles density-matrix dynamics for solids with the inclusion of non-Markovian effects

The theoretical description of materials’ properties driven out of equilibrium has important consequences in various fields such as semiconductor spintronics, nonlinear optics, quantum information science and technology. The coupling of a quantum many-body system to an external bath can dramatically modify its dynamics compared to that of closed systems; new phenomena like relaxation and decoherence appear.

Here we discuss a first-principles methodology based on the evolution of the electron reduced density matrix capable of treating electron-environment interactions and electron-electron correlations at the same level of description [1]. The effect of the environment is separated into a coherent contribution due to polaronic effects and external fields, as well as an incoherent contribution coming from the interaction with lattice vibrations or the thermal background of radiation. Electron-electron interactions are included using the nonequilibrium Green’s function plus generalized Kadanoff-Baym ansatz. The obtained non-Markovian coupled set of equations can be reduced to ordinary Lindblad quantum master equations by taking the Markovian limit via macroscopic time average [2].

We discuss the non-Markovian effects coming from the nonequilibrium phonon dynamics and analyze their influence on the electronic dynamics, by applying this methodology to prototypical realistic systems characterized by strong electron-phonon interactions.

[1] J. Xu, A. Habib, R. Sundararaman, and Y. Ping, Phys. Rev. B 104, 184418 (2021).

[2] J. Simoni, G. Riva, and Y. Ping, J. Chem. Phys. (perspective) , in press (2025), arXiv:2504.17936 [cond-mat.mtrl-sci].