Renormalization group approach to interacting fermion systems in the two-particle-irreducible formalism
| dc.creator | Dupuis, N. | |
| dc.date | 2005-06-21 | |
| dc.date | 2005-11-11 | |
| dc.date.accessioned | 2026-07-07T06:38:01Z | |
| dc.date.available | 2026-07-07T06:38:01Z | |
| dc.description | We describe a new formulation of the functional renormalization group (RG) for interacting fermions within a Wilsonian momentum-shell approach. We show that the Luttinger-Ward functional is a fixed point of the RG, and derive the infinite hierarchy of flow equations satisfied by the two-particle-irreducible (2PI) vertices. In the one-loop approximation, this hierarchy reduces to two equations that determine the self-energy and the 2PI two-particle vertex $Φ^{(2)}$. Susceptibilities are calculated from the Bethe-Salpeter equation that relates them to $Φ^{(2)}$. While the one-loop approximation breaks down at low energy in one-dimensional systems (for reasons that we discuss), it reproduces the exact results both in the normal and ordered phases in single-channel (i.e. mean-field) theories, as shown on the example of BCS theory. The possibility to continue the RG flow into broken-symmetry phases is an essential feature of the 2PI RG scheme and is due to the fact that the 2PI two-particle vertex, contrary to its 1PI counterpart, is not singular at a phase transition. Moreover, the normal phase RG equations can be directly used to derive the Ginzburg-Landau expansion of the thermodynamic potential near a phase transition. We discuss the implementation of the 2PI RG scheme to interacting fermion systems beyond the examples (one-dimensional systems and BCS superconductors) considered in this paper. | |
| dc.description | (v2) 21 pages, 10 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0506542 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0506542 | |
| dc.identifier | Eur.Phys.J. B48 (2005) 319 | |
| dc.identifier | doi:10.1140/epjb/e2005-00409-7 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100592 | |
| dc.subject | Strongly Correlated Electrons | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Renormalization group approach to interacting fermion systems in the two-particle-irreducible formalism | |
| dc.type | text |