arXiv subjects

Sarah Heinzelmann

Publications and source records attributed to Sarah Heinzelmann.

7 recordsLinked to original sources

arXiv2025

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↗

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

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↗

arXiv2023

Mott transition and pseudogap of the square-lattice Hubbard model: results from center-focused cellular dynamical mean-field theory

The recently proposed center-focused post-processing procedure [Phys. Rev. Research 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 $8\times 8$ 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 $4\times 4$ 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.

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.

cond-mat.str-el↗

arXiv2023

Entangled magnetic, charge, and superconducting pairing correlations in the two-dimensional Hubbard model: a functional renormalization-group analysis

Using the recently introduced multiloop extension of the functional renormalization group, we compute the magnetic, density, and superconducting susceptibilities of the two-dimensional Hubbard model at weak coupling and present a detailed analysis of their evolution with temperature, interaction strength, and loop order. By breaking down the susceptibilities into contributions from the bare susceptibility and the individual channels, we investigate their relative importance as well as the channel interplay. In particular, we trace the influence of antiferromagnetic fluctuations on the $d$-wave superconductivity and provide an analytical understanding for the observed behavior.

cond-mat.str-el↗

arXiv2017

Information Dimension of Stochastic Processes on Networks: Relating Entropy Production to Spectral Properties

We consider discrete stochastic processes, modeled by classical master equations, on networks. The temporal growth of the lack of information about the system is captured by its non-equilibrium entropy, defined via the transition probabilities between different nodes of the network. We derive a relation between the entropy and the spectrum of the master equation's transfer matrix. Our findings indicate that the temporal growth of the entropy is proportional to the logarithm of time if the spectral density shows scaling. In analogy to chaos theory, the proportionality factor is called (stochastic) information dimension and gives a global characterization of the dynamics on the network. These general results are corroborated by examples of regular and of fractal networks.

cond-mat.stat-mech↗