Abstract:
We study the phase diagram of the Hubbard model in the limit where U, the onsite repulsive interaction, is much smaller than the bandwidth. We present an asymptotically exact expression for Tc, the superconducting transition temperature, in terms of the correlation functions of the non-interacting system which is valid for arbitrary densities so long as the interactions are sufficiently small. Our strategy for computing Tc involves first integrating out all degrees of freedom having energy higher than an unphysical initial cutoff Ω0. Then, the renormalization group (RG) flows of the resulting effective action are computed and Tc is obtained by determining the scale below which the RG flows in the Cooper channel diverge. We prove that Tc is independent of Ω0.