Nonperturbative renormalization-group approach to fermion systems in the two-particle-irreducible effective action formalism

Understand

We propose a nonperturbative renormalization-group (NPRG) approach to fermion systems in the two-particle-irreducible (2PI) effective action formalism, based on an exact RG equation for the Luttinger-Ward functional.

• This approach enables us to describe phases with spontaneously broken symmetries while satisfying the Mermin-Wagner theorem.
• We show that it is possible to choose the Hartree-Fock--RPA theory as initial condition of the RG flow and argue that the 2PI-NPRG is not restricted to the weak-coupling limit.
• An expansion of the Luttinger-Ward functional about the minimum of the 2PI effective action including only the two-particle 2PI vertex leads to nontrivial RG equations where interactions between fermions and collective excitations naturally emerge.