Stability of correlated electronic systems under the influence of the electron-phonon interaction

TL;DR

This study employs exact diagonalization to analyze how electron-phonon interactions affect the stability of correlated electronic systems, providing more comprehensive insights than previous approximate methods.

Contribution

It introduces an exact diagonalization approach including all phonon modes, improving accuracy over prior frozen-phonon or limited-mode techniques.

Findings

Exact diagonalization confirms previous results within small clusters.

All phonon modes included reveal detailed stability characteristics.

Comparison with adiabatic approximation highlights differences in system behavior.

Abstract

We have used an exact diagonalization technique to study the stability of the $t-J$-Holstein and Hubbard-Holstein models under the influence of the electron-phonon interaction. Previous results have been obtained using frozen-phonon technique or introducing only a few dynamical phonon modes due to the large Hilbert space. To check these results we have done exact diagonalization in a small cluster (four sites) including all the phonon modes allowed by symmetry. We compare our results with those obtained by using the adiabatic approximation.