Abstract
Within a Lagrangian formalism, we derive the time-dependent Gutzwiller approximation for general multi-band Hubbard models. Our approach explicitly incorporates the coupling between time-dependent variational parameters and a time-dependent density matrix from which we obtain dynamical correlation functions in the linear-response regime. Our results are illustrated for the one-band model where we show that the interacting system can be mapped to an effective problem of fermionic quasiparticles coupled to ‘doublon’ (double occupancy) bosonic fluctuations. The latter have an energy on the scale of the on-site Hubbard repulsion U in the dilute limit but become soft at the Brinkman–Rice transition, which is shown to be related to an emerging conservation law of doublon charge and the associated gauge invariance. Coupling with the boson mode produces a structure in the charge response and we find that a similar structure appears in dynamical mean-field theory.
Highlights
Recent advances in ultra-fast spectroscopy allow us to monitor the dynamics of electrons on a femtosecond scale
This approach has recently been generalised for the study of multi-band Hubbard models [12, 13] and is based on the expansion of the Gutzwiller energy functionals which depend on the density matrix and variational parameters related to the atomic eigenstates
For higher densities we study the performance of the time-dependent Gutzwiller approximation (TDGA) by comparing with dynamical mean-field theory (DMFT) and exact diagonalisation results
Summary
Recent advances in ultra-fast spectroscopy allow us to monitor the dynamics of electrons on a femtosecond scale. From the theoretical point of view, this is obviously a challenging problem since it requires a method capable of treating the relaxation dynamics of a strongly correlated system out of equilibrium In this regard, a state-of-the art approach is the dynamical mean-field theory (DMFT) which has recently been applied [4] to the single-band Hubbard model in order to study the doubleoccupancy relaxation after laser excitation. In a series of papers [5, 6, 7, 8], we have developed the TDGA which is based on a variational Ansatz for the Hubbard model [9, 10] evaluated in the limit of infinite spatial dimensions [11] This approach has recently been generalised for the study of multi-band Hubbard models [12, 13] and is based on the expansion of the Gutzwiller energy functionals which depend on the density matrix and variational parameters related to the atomic eigenstates. It has been related to Auger spectroscopy by calculating pair excitations in one- [8] and three-band [20] Hubbard models
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