Mott transition at large orbital degeneracy: Dynamical mean-field theory

We study analytically the Mott transition of the N-orbital Hubbard model using dynamical mean-field theory and a low-energy projection onto an effective Kondo model. It is demonstrated that the critical interaction at which the insulator appears ${(U}_{c1\mathrm{}})$ and the one at which the metal becomes unstable ${(U}_{c2\mathrm{}})$ have a different dependence on the number of orbitals as the latter becomes large: $U_{c1\mathrm{}}\propto \sqrt{N}$ while $U_{c2\mathrm{}}\propto N.\mathrm{}$ An exact analytical determination of the critical coupling $U_{c2\mathrm{}}/N$ is obtained in the large-N limit. The metallic solution close to this critical coupling has many similarities at low-energy with the results of slave boson approximations, to which a comparison is made. We also discuss how the critical temperature associated with the Mott critical endpoint depends on the number of orbitals.