U(1)slave-spin theory and its application to Mott transition in a multiorbital model for iron pnictides

A U(1) slave-spin representation is introduced for multi-orbital Hubbard\nmodels. As with the $Z_2$ form of L. de'Medici et al. (Phys. Rev. B 72, 205124\n(2005)), this approach represents a physical electron operator as the product\nof a slave spin and an auxiliary fermion operator. For non-degenerate\nmulti-orbital models, our U(1) approach is advantageous in that it captures the\nnon-interacting limit at the mean-field level. For systems with either a single\norbital or degenerate multiple orbitals, the U(1) and $Z_2$ slave-spin\napproachs yield the same results in the slave-spin-condensed phase. In general,\nthe U(1) slave-spin approach contains a U(1) gauge redundancy, and properly\ndescribes a Mott insulating phase. We apply the U(1) slave-spin approach to\nstudy the metal-to-insulator transition in a five-orbital model for parent iron\npnictides. We demonstrate a Mott transition as a function of the interactions\nin this model. The nature of the Mott insulating state is influenced by the\ninterplay between the Hund's rule coupling and crystal field splittings. In the\nmetallic phase, when the Hund's rule coupling is beyond a threshold, there is a\ncrossover from a weakly correlated metal to a strongly correlated one, through\nwhich the quasiparticle speactral weight rapidly drops. The existence of such a\nstrongly correlated metallic phase supports the incipient Mott picture of the\nparent iron pnictides. In the parameter regime for this phase and in the\nvicinity of the Mott transition, we find that an orbital selective Mott state\nhas nearly as competitive a ground state energy.\n