Related papers: Parquet approximation and one-loop renormalization…
We demonstrate how to devise a Matsubara-formalism-based one-loop approximation to the flow of the functional renormalization group (FRG) that reproduces identically the leading-logarithmic parquet approximation. This construction of a…
We present a functional renormalization group (fRG) study of the two dimensional Hubbard model, performed with an algorithmic implementation which lifts some of the common approximations made in fRG calculations. In particular, in our fRG…
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.…
Using a leading algorithmic implementation of the functional renormalization group (fRG) for interacting fermions on two-dimensional lattices, we provide a detailed analysis of its quantitative reliability for the Hubbard model. In…
We present a multiloop flow equation for the four-point vertex in the functional renormalization group (fRG) framework. The multiloop flow consists of successive one-loop calculations and sums up all parquet diagrams to arbitrary order.…
We consider the application of the two-loop functional renormalization-group (fRG) approach to study the low-dimensional Hubbard model. This approach accounts for both, the universal and non-universal contributions to the RG flow. While the…
We present multiloop flow equations in the functional renormalization group (fRG) framework for the four-point vertex and self-energy, formulated for a general fermionic many-body problem. This generalizes the previously introduced vertex…
We present a recently-developed renormalization group scheme, the functional renormalization group (fRG), as a many-particle method suited to account for the two-particle interactions between the electrons in complex quantum dot geometries.…
The functional renormalization group (fRG) is an established tool in the treatment of correlated electron systems, notably for the description of competing instabilities. In recent years, methodological advancements led to the multiloop…
The conceptual framework provided by the functional Renormalization Group (fRG) has become a formidable tool to study correlated electron systems on lattices which, in turn, provided great insights to our understanding of complex many-body…
We apply the renormalization-group (RG) approach to two model systems where the two-dimensional Fermi surface has portions which give rise to the logarithmically singular two-loop self-energy process.
This thesis comprises two parts centered around the functional renormalization-group framework: in the first part, I study the role of symmetries and conservation laws in approximate solutions, while in the second part I analyze Friedel…
A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi…
Renormalization group methods are well-established tools for the (numerical) investigation of the low-energy properties of correlated quantum many-body systems, allowing to capture their scale-dependent nature. The functional…
We present a multiloop pseudofermion functional renormalization group (pffRG) approach to quantum spin systems. As a test case, we study the spin-$\tfrac{1}{2}$ Heisenberg model on the kagome lattice, a prime example of a geometrically…
We show that the renormalization group (RG) approach to interacting fermions at one-loop order recovers Fermi liquid theory results when the forward scattering zero sound (ZS) and exchange (ZS$'$) channels are both taken into account. The…
We show how Fermi liquid theory results can be systematically recovered using a renormalization group (RG) approach. Considering a two-dimensional system with a circular Fermi surface, we derive RG equations at one-loop order for the…
The functional renormalization group (FRG), an established computational method for quantum many-body phenomena, has been subject to a diversification in topical applications, analytic approximations and numerical implementations. Despite…
Exact functional renormalization group (FRG) flow equations for quantum systems can be derived directly within an operator formalism without using functional integrals. This simple insight opens new possibilities for applying FRG methods to…
We implement an explicit two-loop calculation of the coupling functions and the self-energy of interacting fermions with a two-dimensional flat Fermi surface in the framework of the field theoretical renormalization group (RG) approach.…