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We compute non-perturbative spectral functions in a scalar $\phi^4$-theory in three spacetime dimensions via the spectral functional renormalisation group. This approach allows for the direct, manifestly Lorentz covariant computation of…
We demonstrate the power of a recently-proposed approximation scheme for the non-perturbative renormalization group that gives access to correlation functions over their full momentum range. We solve numerically the leading-order flow…
We present a general frame to extend functional renormalization group (fRG) based computational schemes by using an exactly solvable interacting reference problem as starting point for the RG flow. The systematic expansion around this…
We present results for in-medium spectral functions obtained within the Functional Renormalization Group framework. The analytic continuation from imaginary to real time is performed in a well-defined way on the level of the flow equations.…
We present first results on the calculation of fermionic spectral functions from analytically continued flow equations within the Functional Renormalization Group approach. Our method is based on the same analytic continuation from…
Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories, and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods…
Renormalisation group approaches are tailor made for resolving the scale-dependence of quantum and statistical systems, and hence their phase structure and critical physics. Usually this advantage comes at the price of having to truncate…
The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for…
We present our progress on a study of the $O(3)$ model in two-dimensions using the Tensor Renormalization Group method. We first construct the theory in terms of tensors, and show how to construct $n$-point correlation functions. We then…
We derive an expansion of the functional renormalization (fRG) equations that treats the frequency and momentum dependencies of the vertices in a systematic manner. The scheme extends the channel-decomposed fRG equations to the frequency…
The functional renormalization group (FRG) approach is a powerful tool for studies of a large variety of systems, ranging from statistical physics over the theory of the strong interaction to gravity. The practical application of this…
In an earlier publication, we have introduced a method to obtain, at large N, the effective action for d-dimensional manifolds in a N-dimensional disordered environment. This allowed to obtain the Functional Renormalization Group (FRG)…
We set up the Functional Renormalisation Group formalism for Tensorial Group Field Theory in full generality. We then apply it to a rank-3 model over U(1) x U(1) x U(1), endowed with a linear kinetic term and nonlocal interactions. The…
We study by the perturbative Functional Renormalization Group (FRG) the Random Field and Random Anisotropy O(N) models near $d=4$, the lower critical dimension of ferromagnetism. The long-distance physics is controlled by zero-temperature…
We employ deep neural networks to represent the field derivative of the scale-dependent effective potential in the functional renormalization group (fRG) framework for nonperturbative quantum field theory. By embedding the fRG flow…
The renormalized trajectory (RT) is determined from two different Monte Carlo renormalization group techniques with $\delta$-function block spin transformation in the multi-dimensional coupling parameter space of the two-dimensional…
We combine two non-perturbative approaches, one based on the two-particle-irreducible (2PI) action, the other on the functional renormalization group (fRG), in an effort to develop new non-perturbative approximations for the field…
We discuss the relation between functional renormalization group (FRG) and local renormalization group (LRG), focussing on the two dimensional case as an example. We show that away from criticality the Wess-Zumino action is described by a…
The functional renormalization group (fRG) approach has the property that, in general, the flow equation for the two-particle vertex generates $\mathcal{O}(N^4)$ independent variables, where $N$ is the number of interacting states (e.g.…
We make an intensive investigation of the soft mode at the quantum chromodynamics (QCD) critical point on the basis of the functional renormalization group (FRG) method in the local potential approximation. We calculate the spectral…