One approach for determining susceptibilities and order parameters in multi-band Hubbard model

We present an approach for determining susceptibilities and order parameters in multi-band Hubbard model within functional renormalization group method, and apply it to study various instabilities of the FeAs-based high temperature superconductor. First, we derive the formulae of susceptibilities and order parameters of superconducting parings, spin density waves and charge density waves with diverse wave vectors which could occur in multi-band Hubbard model. Second, we apply it to the FeAs-based high temperature superconductor and find an electronic-driven superconducting pairing instability within a five band model with pure repulsive interactions. Our study shows that for doping of our concern, there is competition between antiferromagnetic and superconducting instabilities. In addition, we show that for doping of 0.1, the susceptibility of extended s-wave pairing is dominant over others, while a staggered superconducting pairing with has the second largest value of susceptibility.