Slave rotor theory of the Mott transition in the Hubbard model: a new mean field theory and a new variational wave function

A new mean field theory is proposed for the Mott transition in the Hubbard model based on the slave rotor representation of the electron operator. This theory provides a better description of the role of the long range charge correlation in the Mott insulating state and offers a good estimation of the critical correlation strength for the Mott transition. We have constructed a new variational wave function for the Mott insulating state based on this new slave rotor mean field theory. We find this new variational wave function outperforms the conventional Jastrow type wave function with long range charge correlator in the Mott insulating state. It predicts a continuous Mott transition with non-divergent quasiparticle mass at the transition point. We also show that the commonly used on-site mean field decoupling for the slave rotor corresponds to the Gutzwiller approximation for the Gutzwiller projected wave function with only on-site charge correlator, which can not describe the Mott transition in any finite dimensional system.