arXiv subjects

Kilian Fraboulet

Publications and source records attributed to Kilian Fraboulet.

9 recordsLinked to original sources

arXiv2026

Multiloop functional renormalization group from single bosons

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 extension of the fRG, which systematically includes loop corrections beyond the conventional one-loop truncation and yields a quantitatively accurate description of two-dimensional lattice systems. At the same time, the single-boson exchange (SBE) decomposition of the two-particle vertex has been shown to offer both computational and interpretative advantages paving the way to more affordable approximation schemes. We here apply their combination coined as multiloop SBE fRG to the two-dimensional Hubbard model at weak coupling. After providing a detailed account of the underlying formalism in physical channels, we analyze the results for the frequency- and momentum-dependent vertex functions. We find that the SBE approximation, i.e., neglecting the flow of the multi-boson exchange contributions, accurately reproduces the parquet approximation at loop convergence. The presented algorithmic improvement opens the route for the treatment of more challenging parameter regimes and more realistic models.

cond-mat.str-el↗

arXiv2026

Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems

The functional renormalization group (fRG) is acknowledged as a powerful tool in quantum many-body physics and beyond. On the technical side, conventional implementations of the fRG rely on regulators for bare propagators only. Starting from Schwinger--Dyson and Bethe--Salpeter equations, we develop here an fRG formulation where both bare propagators and bare interactions can be dressed with regulators. The approach thus obtained is an extension of the multiloop fRG recently introduced for many-fermion systems. Using the single-boson exchange decomposition, we show that the underlying flow equations are simply interpreted as adding a regulator to the bosonic propagator and that such an extension scarcely changes the original structure of the flow equations. Overall, we provide a framework for implementing approaches that cannot be realized with conventional fRG methods, such as temperature flows for models with retarded interactions. For concrete applications, we analyze the loop convergence of our scheme against conventional cutoff schemes for the Anderson impurity model. Finally, we devise a new temperature-flow scheme that implements a cutoff in both the propagator and the bare interaction, and demonstrate its validity on a model of an Anderson impurity coupled to a phonon.

cond-mat.str-el↗

arXiv2026

BosonFlow: A C++ codebase for dynamic fRG and single-boson exchange in correlated fermion systems

We present a unified C++ implementation of the functional renormalization group and the parquet equations within the single-boson exchange formalism for several paradigmatic tight-binding and impurity models at equilibrium. The implementation computes the full dynamic vertex and self-energies, with momentum dependence treated using a truncated unity framework. We implement multiple self-energy flow equations, cutoff schemes, and extensions ranging from the dynamical functional renormalization group to multiloop flow equations that incorporate cutoffs in both the propagator and the interaction. The codebase serves as a reference for recent developments in the fRG and parquet methods for correlated electron systems and provides a flexible foundation for developing new many-body approaches and extensions.

cond-mat.str-el↗

arXiv2026

Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the functional renormalization group

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.

cond-mat.str-el↗

arXiv2025

Path-integral approaches to strongly-coupled quantum many-body systems

The core of this thesis is the path-integral formulation of quantum field theory and its ability to describe strongly-coupled quantum many-body systems of finite size. Collective behaviors can be efficiently described in such systems through the implementation of spontaneous symmetry breaking (SSB) in mean-field approaches. However, as the thermodynamic limit does not make sense in finite-size systems, the latter can not exhibit any SSB and the symmetries which are broken down at the mean-field level must therefore be restored. The efficiency of theoretical approaches in the treatment of finite-size quantum systems can therefore be studied via their ability to restore spontaneously broken symmetries. In this thesis, a zero-dimensional $O(N)$ model is taken as a theoretical laboratory to perform such an investigation with many state-of-the-art path-integral techniques: perturbation theory combined with various resummation methods (Padé-Borel, Borel-hypergeometric, conformal mapping), enhanced versions of perturbation theory (transseries derived via Lefschetz thimbles, optimized perturbation theory), self-consistent perturbation theory based on effective actions (auxiliary field loop expansion (LOAF), Cornwall-Jackiw-Tomboulis (CJT) formalism, 4PPI effective action, ...), functional renormalization group (FRG) techniques (FRG based on the Wetterich equation, DFT-FRG, 2PI-FRG). Connections between these different techniques are also emphasized. In addition, the path-integral formalism provides us with the possibility to introduce collective degrees of freedom in an exact fashion via Hubbard-Stratonovich transformations: the effect of such transformations on the aforementioned methods is also examined in detail.

cond-mat.str-el↗

arXiv2024

Screening and effective RPA-like charge susceptibility in the extended Hubbard model

We generalize the recently introduced single-boson exchange formalism to nonlocal interactions. In the functional renormalization group application to the extended Hubbard model in two dimensions, we show that the flow of the rest function can be neglected up to moderate interaction strengths. We explore the physics arising from the interplay between onsite and nearest-neighbor interactions in various parameter regimes by performing a fluctuation diagnostics. Differently from the magnetic and superconducting susceptibilities, the charge susceptibility appears to be described by the random phase approximation (RPA). We show that this behavior can be traced back to cancellations in the renormalization of the density fermion-boson coupling.

cond-mat.str-el↗

arXiv2024

Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric $φ^{4}$-theory

The energy density functional (EDF) method is currently the only microscopic theoretical approach able to tackle the entire nuclear chart. Nevertheless, it suffers from limitations resulting from its empirical character and deteriorating its reliability. This paper is part of a larger program that aims at formulating the EDF approach as an effective field theory (EFT) in order to overcome these limitations. A relevant framework to achieve this is the path-integral (PI) formulation of quantum field theory (QFT). The latter indeed provides a wide variety of treatments of the many-body problem well suited to deal with non-perturbative interactions and to exploit a Lagrangian resulting from an EFT as a starting point. While developing the formalism in a general setting, we present a comparative study of such techniques applied to a toy model, i.e. the (0+0)-D $O(N)$-symmetric $φ^{4}$-theory. More specifically, our focus will be on the following diagrammatic techniques: loop expansion (LE), optimized perturbation theory (OPT) and self-consistent perturbation theory (SCPT). With these methods, we notably address the spontaneous breakdown of the $O(N)$ symmetry with care especially since spontaneous symmetry breakings (SSBs) play a paramount role in current implementations of the EDF approach.

nucl-th↗

arXiv2024

Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric $φ^{4}$-theory

The present paper is the second of a series of publications that aim at investigating relevant directions to turn the nuclear energy density functional (EDF) method as an effective field theory (EFT). The EDF approach has known numerous successes in nuclear theory over the past decades and is currently the only microscopic technique that can be applied to all atomic nuclei. However, the phenomenological character of the EDF method also comes with important limitations, such as the lack of an explicit connection with quantum chromodynamics (QCD). As was argued in the first paper of this series, reformulating the EDF framework as an EFT would enable us to overcome these limitations. In particular, path-integral (PI) techniques are suited to achieve such a purpose as they allow to design numerous non-perturbative approximations and can take Lagrangians possibly derived from EFTs of QCD as inputs. In our previous paper, we have illustrated such technical features for diagrammatic PI techniques in a study of the (0+0)-D $O(N)$-symmetric $φ^{4}$-theory. In the present work, we consider another class of PI techniques, i.e. functional renormalization group (FRG) approaches, that we apply to the same toy model. Despite our explicit interest for the nuclear many-body problem, the presented study is also directed towards FRG practitioners from various fields: technical details are provided for FRG techniques based on 1-particle-irreducible (1PI), 2-particle-irreducible (2PI) and 2-particle-point-irreducible (2PPI) effective actions (EAs), coined respectively as 1PI-, 2PI- and 2PPI-FRGs, and the treatment of the $O(N)$ symmetry is also addressed thoroughly. Connections between these various FRG methods are identified as well.

cond-mat.str-el↗

arXiv2023

Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling

We illustrate the algorithmic advantages of the recently introduced single-boson exchange (SBE) formulation for the one-loop functional renormalization group (fRG), by applying it to the two-dimensional Hubbard model on a square lattice. We present a detailed analysis of the fermion-boson Yukawa couplings and of the corresponding physical susceptibilities by studying their evolution with temperature and interaction strength, both at half filling and finite doping. The comparison with the conventional fermionic fRG decomposition shows that the rest functions of the SBE algorithm, which describe correlation effects beyond the SBE processes, play a negligible role in the weak-coupling regime above the pseudo-critical temperature, in contrast to the rest functions of the conventional fRG. Remarkably, they remain finite also at the pseudo-critical transition, whereas the corresponding rest functions of the conventional fRG implementation diverge. As a result, the SBE formulation of the fRG flow allows for a substantial reduction of the numerical effort in the treatment of the two-particle vertex function, paving a promising route for future multiboson and multiloop extensions.

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