Electron Dynamics with the Time-Dependent Density Matrix Renormalization Group

TL;DR

This paper introduces a TD-DMRG computational framework for simulating electron dynamics in molecular systems, enabling accurate modeling of complex phenomena like polarizabilities, spectra, and ionization.

Contribution

It develops a tangent-space TD-DMRG method parametrized as a matrix product state for precise electron dynamics simulation with the exact electronic Hamiltonian.

Findings

Simulates systems with up to 20 electrons and 32 orbitals.

Accurately computes molecular (hyper)polarizabilities.

Models electronic absorption spectra and ultrafast ionization dynamics.

Abstract

In this work, we simulate the electron dynamics in molecular systems with the Time-Dependent Density Matrix Renormalization Group (TD-DMRG) algorithm. We leverage the generality of the so-called tangent-space TD-DMRG formulation and design a computational framework in which the dynamics is driven by the exact non-relativistic electronic Hamiltonian. We show that, by parametrizing the wave function as a matrix product state, we can accurately simulate the dynamics of systems including up to 20 electrons and 32 orbitals. We apply the TD-DMRG algorithm to three problems that are hardly targeted by time-independent methods: the calculation of molecular (hyper)polarizabilities, the simulation of electronic absorption spectra, and the study of ultrafast ionization dynamics.