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

TL;DR

This paper investigates how electron correlations affect phonon frequency renormalization in strongly correlated systems using the time-dependent Gutzwiller approximation, revealing contrasting effects for local and non-local couplings and identifying phase separation phenomena.

Contribution

It introduces a detailed analysis of phonon renormalization in correlated systems with local and transitive electron-lattice couplings using TDGA, highlighting new mechanisms and effects.

Findings

Local Holstein coupling weakens phonon frequency renormalization with increasing U.

SSH-Hubbard model shows enhanced phonon shifts at small wave-vectors due to correlations.

Strong correlations induce a shift to q=0 instability, leading to phase separation.

Abstract

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.