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

Abstract

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.

v1) 22 pages, 6 figures, v2) typos corrected, references added

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• The (extended) dynamical mean field theory combined with the two-particle irreducible functional renormalization-group approach as a tool to study strongly-correlated systems
• A Non-Perturbative Renormalization Group approach to quantum XY spin models
• Renormalization group flow of the Luttinger-Ward functional: conserving approximations and application to the Anderson impurity model
• Effects of Renormalizing the chiral SU(2) Quark-Meson-Model
• Quasi-condensation in two-dimensional Fermi gases
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• Wave propagation in non Gaussian random media
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
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• The quantum $p$-spin renormalization group in the large $N$ limit as a benchmark for functional renormalization group
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