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

Abstract

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.

9 pages, 4 figures, puplished version

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• Nonlocal effective average action approach to crystalline phantom membranes
• Renormalization group for phases with broken discrete symmetry near quantum critical points
• Non-perturbative renormalization-group approach to lattice models
• Dynamic structure factor of Luttinger liquids with quadratic energy dispersion and long-range interactions
• Effective average action based approach to correlation functions at finite momenta
• Condensate density of interacting bosons: a functional renormalization group approach