Influence of electron-phonon interaction on quantum phase transition in a triangular triple quantum dot

We investigate the quantum phase transition in triple quantum dot system with triangular geometry, in which one of the dots is connected to metallic leads and electrons in the dot interact with a local phonon mode. The influence of electron-phonon interaction on the quantum phase transition between local moment phase and Kondo screened strong coupling phase at the particle-hole symmetric point is studied based on the analytical arguments and the numerical renormalization group method. The results show that the critical value of tunnel-coupling between side dots decreases with the increase of electron-phonon coupling in “spin Kondo” regime. Furthermore, at a certain critical value of electron-phonon coupling, there appears only strong coupling phase, irrespective of tunnel-coupling between dots. The study of the influence of electron-phonon interaction on the quantum phase transition in triple quantum dot has the great importance for clarifying the mechanism of Kondo screening in the system.