Ab-initio variational wave functions for the time-dependent many-electron Schrödinger equation

Describing the real-time evolution of many-electron quantum systems is crucial for understanding the dynamical properties of condensed matter, molecular systems in quantum chemistry, and the behaviors of complex materials. However, the real-time evolution of non-equilibrium quantum electronic systems poses a significant challenge for theoretical and computational approaches. This work introduces a variational approach for fermionic time-dependent wave functions, surpassing mean-field approximations by capturing many-body correlations. Our methodology introduces a parameterization of the time-evolving quantum state, enabling an accurate approximation of its evolution. To account for electron correlations, we employ time-dependent Jastrow factors and backflow transformations, which can be further enhanced by incorporating neural networks for function parameterization. We utilize the time-dependent variational Monte Carlo technique to efficiently compute optimal time-dependent parameters. Additionally, we introduce a new time-evolution method based on Trotter-root expansions of the propagator, enhancing the accuracy and efficiency of our simulations. The approach is demonstrated in three distinct systems: the solvable harmonic interaction model, the dynamics of a diatomic molecule in intense laser fields, and a quenched quantum dot. In all cases, we show clear signatures of many-body correlations in the dynamics that are not captured by mean-field methods. The results showcase the ability of our variational approach to accurately capture the time evolution of quantum states, providing insight into the quantum dynamics of interacting electronic systems, beyond the capabilities of mean-field.