Contributor info: Prof. Sabine Andergassen

Miriam Patricolo, Marcel Gievers, Kilian Fraboulet, Aiman Al-Eryani, Sarah Heinzelmann, Pietro M. Bonetti, Alessandro Toschi, Demetrio Vilardi, Sabine Andergassen

SciPost Phys. 18, 078 (2025) · published 4 March 2025 | Toggle abstract · pdf

We extend the recently introduced single-boson exchange formulation to the computation of the self-energy from the Schwinger–Dyson equation (SDE). In particular, we derive its expression both in diagrammatic and in physical channels. The simple form of the single-boson exchange SDE, involving only the bosonic propagator and the fermion-boson vertex, but not the rest function, allows for an efficient numerical implementation. We furthermore discuss its implications in a truncated unity solver, where a restricted number of form factors introduces an information loss in the projection of the momentum dependence that in general affects the equivalence between the different channel representations. In the application to the functional renormalization group, we find that the convergence in the number of form factors depends on the channel representation of the SDE. For the two-dimensional Hubbard model at weak coupling, the pseudogap opening driven by antiferromagnetic fluctuations is captured already by a single ($s$-wave) form factor in the magnetic channel representation, differently to the density and superconducting channels.

Michael Meixner, Henri Menke, Marcel Klett, Sarah Heinzelmann, Sabine Andergassen, Philipp Hansmann, Thomas Schäfer

SciPost Phys. 16, 059 (2024) · published 27 February 2024 | Toggle abstract · pdf

The recently proposed center-focused post-processing procedure [Phys. Rev. Res. 2, 033476 (2020)] of cellular dynamical mean-field theory suggests that central sites of large impurity clusters are closer to the exact solution of the Hubbard model than the edge sites. In this paper, we systematically investigate results in the spirit of this center-focused scheme for several cluster sizes up to 8×8 in and out of particle-hole symmetry. First we analyze the metal-insulator crossovers and transitions of the half-filled Hubbard model on a simple square lattice. We find that the critical interaction of the crossover is reduced with increasing cluster sizes and the critical temperature abruptly drops for the 4×4 cluster. Second, for this cluster size, we apply the center-focused scheme to a system with more realistic tight-binding parameters, investigating its pseudogap regime as a function of temperature and doping, where we find doping dependent metal-insulator crossovers, Lifshitz transitions and a strongly renormalized Fermi-liquid regime. Additionally to diagnosing the real space origin of the suppressed antinodal spectral weight in the pseudogap regime, we can infer hints towards underlying charge ordering tendencies.

Agnese Tagliavini, Cornelia Hille, Fabian B. Kugler, Sabine Andergassen, Alessandro Toschi, Carsten Honerkamp

SciPost Phys. 6, 009 (2019) · published 18 January 2019 | Toggle abstract · pdf

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 flow; (i) we take explicitly into account the momentum and the frequency dependence of the vertex functions; (ii) we include the feedback effect of the self-energy; (iii) we implement the recently introduced multiloop extension which allows us to sum up {\emph{all}} the diagrams of the parquet approximation with their exact weight. Due to its iterative structure based on successive one-loop computations, the loop convergence of the fRG results can be obtained with an affordable numerical effort. In particular, focusing on the analysis of the physical response functions, we show that the results become {\emph{independent}} from the chosen cutoff scheme and from the way the fRG susceptibilities are computed, i.e., either through flowing couplings to external fields, or through a "post-processing" contraction of the interaction vertex at the end of the flow. The presented substantial refinement of fRG-based computation schemes paves a promising route towards future quantitative fRG analyses of more challenging systems and/or parameter regimes.