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

摘要

We propose a nonperturbative renormalization-group (NPRG) approach to fermionsystems in the two-particle-irreducible (2PI) effective action formalism, basedon an exact RG equation for the Luttinger-Ward functional. This approachenables us to describe phases with spontaneously broken symmetries whilesatisfying the Mermin-Wagner theorem. We show that it is possible to choose theHartree-Fock--RPA theory as initial condition of the RG flow and argue that the2PI-NPRG is not restricted to the weak-coupling limit. An expansion of theLuttinger-Ward functional about the minimum of the 2PI effective actionincluding only the two-particle 2PI vertex leads to nontrivial RG equationswhere interactions between fermions and collective excitations naturallyemerge.