Functional renormalization group in the broken symmetry phase: momentum dependence and two-parameter scaling of the self-energy

We include spontaneous symmetry breaking into the functional renormalization group (RG) equations for the irreducible vertices of Ginzburg-Landau theories by augmenting these equations by a flow equation for the order parameter, which is determined from the requirement that at each RG step the vertex with one external leg vanishes identically. Using this strategy, we propose a simple truncation of the coupled RG flow equations for the vertices in the broken symmetry phase of the Ising universality class in D dimensions. Our truncation yields the full momentum dependence of the self-energy Sigma (k) and interpolates between lowest order perturbation theory at large momenta k and the critical scaling regime for small k. Close to the critical point, our method yields the self-energy in the scaling form Sigma (k) = k_c^2 sigma^{-} (k | xi, k / k_c), where xi is the order parameter correlation length, k_c is the Ginzburg scale, and sigma^{-} (x, y) is a dimensionless two-parameter scaling function for the broken symmetry phase which we explicitly calculate within our truncation.Comment: 9 pages, 4 figures, puplished versio

Non-perturbative renormalization-group approach to zero-temperature Bose systems

We use a non-perturbative renormalization-group technique to study interacting bosons at zero temperature. Our approach reveals the instability of the Bogoliubov fixed point when $d\leq 3$ and yields the exact infrared behavior in all dimensions $d>1$ within a rather simple theoretical framework. It also enables to compute the low-energy properties in terms of the parameters of a microscopic model. In one-dimension and for not too strong interactions, it yields a good picture of the Luttinger-liquid behavior of the superfluid phase.Comment: v1) 6 pages, 8 figures; v2) added references; v3) corrected typo