Linear-Response Dynamics from the Time-Dependent Gutzwiller Approximation

TL;DR

This paper develops a time-dependent Gutzwiller approximation for multi-band Hubbard models, linking variational parameters with density matrices to analyze dynamical correlations and quasiparticle interactions.

Contribution

It introduces a Lagrangian formalism that explicitly couples variational parameters with density matrices in the time-dependent Gutzwiller approach for complex Hubbard models.

Findings

Mapping of the interacting system to fermionic quasiparticles coupled to doublon fluctuations.

Identification of a soft mode at the Brinkman-Rice transition related to doublon conservation.

Structural features in charge response similar to dynamical mean-field theory results.

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 becomes 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 structure in the charge response and we find that a similar structure appears in dynamical mean-field theory.