Effect of Local Jahn-Teller Phonons on Quantum Critical Point in a Two-Orbital Anderson Model

We investigate the emergence of quantum critical point (QCP) in two-orbital Anderson models with and without local Jahn-Teller phonons by employing a numerical renormalization group method. Throughout this work, we consider the half -filling case at an impurity site, in which local electron number n is set as n = 2. For the case without Jahn-Teller phonons, we reconfirm the existence of the QCP between local singlet and Kondo singlet phases, irrespective of the origin of the Kondo singlet formation, namely, the spin Kondo in Gamma 5 or the orbital Kondo effect in Gamma 3. Next we consider the case with Jahn-Teller phonons, in which Gamma 3 state is changed to the vibronic doublet phase characterized by the rotation direction, clockwise or anti-clockwise, of total angular momentum. Also in this case, we again observe the QCP between the local singlet and Kondo singlet phases, but when we depict the QCP curve on a parameter plane, we remark the difference in the form of the QCP curve from the case without Jahn-Teller phonons. We discuss a possible origin of such difference. Finally, we provide a brief comment on the observation of the present QCP in actual materials.