Papers

This study, led by my colleague Markus Frankenbach, introduces a practical way to deal with the enormous datasets that come out of modern quantum many-body calculations. By applying a compression technique known as quantics tensor cross interpolation, we show that it’s possible to represent complex four-point correlation functions from the multipoint numerical renormalization group in a compact and accurate form. Tested on the single-impurity Anderson model, this approach cuts memory and computational costs dramatically without sacrificing precision, paving the way for more advanced methods to tackle strongly correlated electron systems.

In this paper, we investigate the accuracy of the multipoint numerical renormalization group, a new computational approach for studying strongly interacting quantum systems. We calculate two- and four-point correlation functions for the single-impurity Anderson model, and then test these results against exact consistency conditions from quantum field theory. By checking equations such as the parquet equations and the U(1) Ward identity, we show that the method reliably reproduces fundamental constraints, even in challenging regimes. This work strengthens confidence in the technique as a foundation for future studies of complex electronic materials.

In this article, we introduce KeldyshQFT, a high‑performance C++ toolkit for studying interacting electrons in impurity models. Working directly in real frequencies using Keldysh quantum field theory, it produces results that compare more faithfully to experiments than imaginary‑time methods. The software unites two advanced approaches—the multiloop functional renormalization group and the self‑consistent parquet equations—engineered for speed with vectorization, OpenMP/MPI parallelism, and optimized data layouts. It supports self‑energy feedback, multiple regulators, and arbitrary loop order, and scales efficiently on CPUs. The article also details modular design choices that aid flexibility, testing, and future extensions.

The code can be found here:  github.com/NepomukRitz/KeldyshQFT 

* shared first authorship

Understanding how strongly interacting electrons behave is crucial for modern physics, but calculating their real-frequency response functions is notoriously difficult. In this work, we apply quantum field theory to the single-impurity Anderson model using the Keldysh formalism, which directly accesses real-frequency data and avoids the pitfalls of analytic continuation. We improve functional renormalization group calculations by introducing a parametrization that fully captures the frequency dependence of the four-point vertex, and we solve the parquet equations in the parquet approximation. Compared to benchmark results, our methods show significantly improved accuracy and open the door to tackling more complex models.

* shared first authorship

This work, led by Dominik Kiese, introduces MatsubaraFunctions.jl, a Julia library designed to make advanced quantum field theory calculations more accessible and efficient. The package provides flexible data structures for handling generalized Green’s functions on Matsubara frequency grids, a key tool for studying interacting quantum systems at finite temperatures. Its design balances ease of use with the ability to develop high-performance solvers, supporting features such as interpolation, extrapolation, symmetry handling, and parallelization. Through a range of illustrative examples, we demonstrate how the library streamlines complex workflows and helps researchers avoid common performance bottlenecks, paving the way for more efficient simulations in equilibrium quantum many-body physics.

The code can be found here: github.com/dominikkiese/MatsubaraFunctions.jl