Phonon renormalization from local and transitive electron-lattice couplings in strongly correlated systems

Within the time-dependent Gutzwiller approximation (TDGA) applied to Holstein- and SSH-Hubbard models we study the influence of electron correlations on the phonon self-energy. For the local Holstein coupling we find that the phonon frequency renormalization gets weakened upon increasing the onsite interaction $U$ for all momenta. In contrast, correlations can enhance the phonon frequency shift for small wave-vectors in the SSH-Hubbard model. Moreover the TDGA applied to the latter model provides a mechanism which leads to phonon frequency corrections at intermediate momenta due to the coupling with double occupancy fluctuations. Both models display a shift of the nesting-induced to a $q=0$ instability when the onsite interaction becomes sufficiently strong and thus establishing phase separation as a generic phenomenon of strongly correlated electron-phonon coupled systems.Comment: 14 pages, 11 figure

Time-Dependent Gutzwiller Theory for Multiband Hubbard Models

Based on the variational Gutzwiller theory, we present a method for the computation of response functions for multiband Hubbard models with general local Coulomb interactions. The improvement over the conventional random-phase approximation is exemplified for an infinite-dimensional two-band Hubbard model where the incorporation of the local multiplet-structure leads to a much larger sensitivity of ferromagnetism on the Hund coupling. Our method can be implemented into LDA+Gutzwiller schemes and will therefore be an important tool for the computation of response functions for strongly correlated materials.Comment: 4 pages, 3 figure