We investigate the phase diagram of two-component fermions in the BCS-BEC crossover. Using functional renormalization group equations we calculate the effect of quantum fluctuations on the fermionic self-energy parametrized by a wavefunction renormal
ization, an effective Fermi radius and the gap. This allows us to follow the modifications of the Fermi surface and the dispersion relation for fermionic excitations throughout the whole crossover region. We also determine the critical temperature of the second order phase transition to superfluidity. Our results are in agreement with BCS theory including Gorkovs correction for small negative scattering length a and with an interacting Bose gas for small positive a. At the unitarity point the result for the gap at zero temperature agrees well with Quantum-Monte-Carlo simulations while the critical temperature differs.
We propose an exact flow equation for composite operators and their correlation functions. This can be used for a scale-dependent partial bosonization or flowing bosonization of fermionic interactions, or for an effective change of degrees of freedom
in dependence on the momentum scale. The flow keeps track of the scale dependent relation between effective composite fields and corresponding composite operators in terms of the fundamental fields.
