Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods.

We benchmark a set of quantum-chemistry methods, including multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest dynamics, against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method, in general, only captures the ultrashort time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.

Merging Features from Green's Functions and Time Dependent Density Functional Theory: A Route to the Description of Correlated Materials out of Equilibrium?

We propose a description of nonequilibrium systems via a simple protocol that combines exchange-correlation potentials from density functional theory with self-energies of many-body perturbation theory. The approach, aimed to avoid double counting of interactions, is tested against exact results in Hubbard-type systems, with respect to interaction strength, perturbation speed and inhomogeneity, and system dimensionality and size. In many regimes, we find significant improvement over adiabatic time dependent density functional theory or second Born nonequilibrium Green's function approximations. We briefly discuss the reasons for the residual discrepancies, and directions for future work.

Probing strongly correlated materials in non-equilibrium: basic concepts and possible future trends in first principle approaches.

Time-resolved spectroscopy has an emerging role among modern material-characterization techniques. Two powerful theoretical formalisms for systems out of equilibrium (and thus for time-resolved spectroscopy) are Non-Equilibrium Green's Functions (NEGF) and Time-Dependent Density Functional Theory (TDDFT). In this chapter, we offer a perspective (with more emphasis on the NEGF) on their current capability to deal with the case of strongly correlated materials. To this end, the NEGF technique is briefly presented, and its use in time-resolved spectroscopy highlighted. We then show how a linear response description is recovered from NEGF real-time dynamics. This is followed by a review of a recent ab initio NEGF treatment and by a short introduction to TDDFT. With these background notions, we turn to the problem of describing strong correlation effects by NEGF and TDDFT. This is done in terms of model Hamiltonians: using simple lattice systems as benchmarks, we illustrate to what extent NEGF and TDDFT can presently describe complex materials out of equilibrium and with strong electronic correlations. Finally, an outlook is given on future trends in NEGF and TDDFT research of interest to time-resolved spectroscopy.