Functional Renormalization Group Treatment Research Articles

On the Lorentz symmetry in conformally reduced quantum gravity

The functional renormalization group treatment of the conform reduced Einstein–Hilbert gravity is extended by following the evolution of the time and space derivatives separately, in order to consider the Lorentz symmetry during the evolution. We found the Reuter fixed point in the ultraviolet region. It is shown that starting from the Gaussian fixed point the Lorentz symmetry breaks down in the vicinity of the Reuter fixed point. Similarly, in the broken phase it also breaks down in the infrared region close to a critical singularity scale. By calculating the anomalous dimension form the kinetic term of the action, we found a new relevant coupling belonging to the curvature.

Renormalization of the bilocal sine-Gordon model

The functional renormalization group treatment is presented for the two-dimensional sine-Gordon model including a bilocal term in the potential, which contributes to the flow at the tree level. It is shown that the flow of the bilocal term can substitute the evolution of the wave function renormalization constant, since it can recover the Kosterlitz–Thouless type phase transition. The flows can also reveal the connection between the sine-Gordon and the noninteracting Thirring models at a special value of the wave number parameter.

Renormalization of Lorentzian conformally reduced gravity

The functional renormalization group treatment is presented for the conformally reduced form of the quantum Einstein gravity with Lorentzian signature. It is shown that the model is asymptotically safe. The critical exponents are determined for various types of regulators.

Functional renormalization group treatment of the 0.7 analog in quantum point contacts

We use a recently developed fRG method (extendend Coupled-Ladder Approximation) to study the 0.7-analog in quantum point contacts, arising at the crossing of the 1st and 2nd band at suf- ficiently high magnetic fields. We reproduce the main features of the experimentally observed magnetic field dependence of the conductance at the 0.7-analog, using a QPC model with two bands and short-range interactions. In particular, we reproduce the fact that this dependence is quali- tatively different, depending on whether the analog is approached from higher or lower magnetic fields. We show that this effect can be explained qualitatively within a simple Hartree picture for the influence of the lowest electrons.

Second-order functional renormalization group approach to one-dimensional systems in real and momentum space

We devise a functional renormalization group treatment for a chain of interacting spinless fermions which is correct up to second order in the interaction strength. We treat both inhomogeneous systems in real-space as well as the translational invariant case in a k-space formalism. The strengths and shortcomings of the different schemes as well as technical details of their implementation are discussed. We use the method to study two proof-of-principle problems in the realm of Luttinger liquid physics, namely reflection at interfaces and power laws in the occupation number as a function of crystal momentum.

Functional renormalization group study of an eight-band model for the iron arsenides

We investigate the superconducting pairing instabilities of eight-band models for the iron arsenides. Using a functional renormalization group treatment, we determine how the critical energy scale for superconductivity depends on the electronic band structure. Most importantly, if we vary the parameters from values corresponding to LaFeAsO to SmFeAsO, the pairing scale is strongly enhanced, in accordance with the experimental observation. We analyze the reasons for this trend and compare the results of the eight-band approach to those found using five-band models.

Critical exponents of theO(N)model in the infrared limit from functional renormalization

We determined the critical exponent $\nu$ of the scalar O(N) model with a strategy based on the definition of the correlation length in the infrared limit. The functional renormalization group treatment of the model shows that there is an infrared fixed point in the broken phase. The appearing degeneracy induces a dynamical length scale there, which can be considered as the correlation length. It is shown that the IR scaling behavior can account either for the Ising type phase transition in the 3-dimensional O(N) model, or for the Kosterlitz-Thouless type scaling of the 2-dimensional O(2) model.

The Functional Renormalization Group Treatment of Disordered Systems, a Review

We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group treatment is necessary, contrary to pure systems, where renormalization of a single coupling constant is sufficient. This leads to a disorder distribution, which after a finite renomalization becomes non-analytic, thus overcoming the predictions of the seemingly exact dimensional reduction. We discuss, how a renormalizable field theory can be constructed, even beyond 1-loop order. We then discuss an elastic manifold imbedded in N dimensions, and give the exact solution for N -> oo. This is compared to predictions of the Gaussian replica variational ansatz, using replica symmetry breaking. We finally discuss depinning, both isotropic and anisotropic, and the scaling function for the width distribution of an interface.

Weak charge quantization on a superconducting island

We consider Coulomb blockade on a superconductive quantum dot strongly coupled to a lead through a tunneling barrier and/or normal diffusive metal. Andreev transport of the correlated pairs leads to quantum fluctuations of the charge on the dot. These fluctuations result in exponential renormalization of the effective charging energy. We employ two complimentary ways to approach the problem: the instanton and the functional renormalization group treatment of the nonlinear $\ensuremath{\sigma}$ model. We show that these two different methods produce identical results. We also derive the charging energy renormalization in terms of the arbitrary transmission matrix of the multichannel interface.

Velocity-force characteristics of a driven interface in a disordered medium

Using a dynamic functional renormalization group treatment of driven elastic interfaces in a disordered medium, we investigate several aspects of the creep-type motion induced by external forces below the depinning threshold $f_c$: i) We show that in the experimentally important regime of forces slightly below $f_c$ the velocity obeys an Arrhenius-type law $v\sim\exp[-U(f)/T]$ with an effective energy barrier $U(f)\propto (f_{c}-f)$ vanishing linearly when f approaches the threshold $f_c$. ii) Thermal fluctuations soften the pinning landscape at high temperatures. Determining the corresponding velocity-force characteristics at low driving forces for internal dimensions d=1,2 (strings and interfaces) we find a particular non-Arrhenius type creep $v\sim \exp[-(f_c(T)/f)^{\mu}]$ involving the reduced threshold force $f_c(T)$ alone. For d=3 we obtain a similar v-f characteristic which is, however, non-universal and depends explicitly on the microscopic cutoff.