arXiv subjects

Niklas Zorbach

Publications and source records attributed to Niklas Zorbach.

7 recordsLinked to original sources

arXiv2026

Analysis of regulator and cutoff artifacts in the phase diagram of the quark-meson model

We study regulator and cutoff artifacts in the quark-meson model at finite temperature and quark chemical potential within the functional renormalization-group approach using the local potential approximation. To this end, we discuss the concept of renormalization-group consistency in effective models, which necessitates a nontrivial parameter-fixing procedure to enable a meaningful comparison of results obtained with different regulators and cutoffs. We employ a standard range of cutoff values used in phenomenological studies and regulators that differ significantly in their analytic properties as well as in their classification according to the principle of strongest singularity. We find that regulator and cutoff dependences are small at low temperatures and quark chemical potentials. At high temperatures and low quark chemical potentials, significant cutoff artifacts arise, whereas the properties of the regulator affect the dynamics in the regime governed by a chiral phase transition of first order at low temperatures and high quark chemical potentials.

hep-ph↗

arXiv2025

Nonperturbative fluctuation effects of charged bosonic fields: A quark-diquark model study at nonzero density

We study the renormalization group flow of the scale-dependent effective potential of a quark-diquark model with full field dependence at nonzero chemical potential. This includes a discussion of approximations in relation to complex bosonic fields and the Silver-Blaze property. The resulting flow equation for the scale-dependent effective potential can in principle be solved down to the infrared limit. For our quark-diquark model, which may serve as a low-energy model for dense strong-interaction matter, we find that a competition between the Bardeen-Cooper-Schrieffer singularity and bosonic fluctuations can trigger a first-order phase transition at low temperatures that turns into a second-order phase transition at a tricritical point as the temperature increases.

hep-ph↗

arXiv2025

Lattice Monte Carlo meets lattice functional Renormalization Group: A quantitative comparison

Lattice Monte Carlo (MC) simulations and the functional Renormalization Group (RG) are powerful approaches that allow for quantitative studies of non-perturbative phenomena such as bound-state formation, spontaneous symmetry breaking and phase transitions. While results from both methods have recently shown remarkable agreement for many observables, e.g., in Quantum Chromodynamics, an analysis of deviations in certain quantities turns out to be challenging. This is because calculations with the two methods are based on different approximations, regularizations and scale fixing procedures. In the present work, we present a framework for a more direct comparison by formulating the functional RG approach on a finite spacetime lattice. This removes all ambiguities of regularization, finite size and scale fixing procedures in concrete studies. By investigating the emergence of spontaneous symmetry breaking and phase transitions in a $Z(2)$ scalar theory in $d=1,2,3$ spacetime dimensions, we demonstrate at the example of the local potential approximation how this framework can be used to evaluate and compare the systematic errors of both approaches.

hep-lat↗

arXiv2024

Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space

Within the Functional Renormalisation Group (FRG) approach, we present a fluid-dynamical approach to solving flow equations for models living in a multi-dimensional field space. To this end, the underlying exact flow equation of the effective potential is reformulated as a set of nonlinear advection-diffusion-type equations which can be solved using the Kurganov-Tadmor central scheme, a modern finite-volume discretization from computational fluid dynamics (CFD). We demonstrate the effectiveness of our approach by performing explicit benchmark tests using zero-dimensional models with two discretized field space directions or two symmetry invariants. Our techniques can be directly applied to flow equations of effective potentials of general (fermion-)boson systems with multiple invariants or condensates, as we also demonstrate for two concrete examples in three spacetime dimensions.

cond-mat.stat-mech↗

arXiv2024

Optimization and Stabilization of Functional Renormalization Group Flows

We revisit optimization of functional renormalization group flows by analyzing regularized loop integrals. This leads us to a principle, the Principle of Strongest Singularity, and a corresponding order relation which allows to order existing regularization schemes with respect to the stability of renormalization group flows. Moreover, the order relation can be used to construct new regulators in a systematic fashion. For studies of critical behavior, which require to follow renormalization group flows down to the deep infrared regime, such new regulators may turn out to be particularly useful. The general application of this principle is demonstrated with the aid of a scalar field theory which is solved over a wide range of scales with novel methods borrowed from numerical fluid dynamics.

hep-ph↗

arXiv2024

Solving the Lindblad equation with methods from computational fluid dynamics

Liouvillian dynamics describes the evolution of a density operator in closed quantum systems. One extension towards open quantum systems is provided by the Lindblad equation. It is applied to various systems and energy regimes in solid state physics as well as also in nuclear physics. A main challenge is that analytical solutions for the Lindblad equation are only obtained for harmonic system potentials or two-level systems. For other setups one has to rely on numerical methods. In this work, we propose to use a method from computational fluid dynamics, the Kurganov-Tadmor central (finite volume) scheme, to numerically solve the Lindblad equation in position-space representation. We will argue, that this method is advantageous in terms of the efficiency concerning initial conditions, discretization, and stability. On the one hand, we study, the applicability of this scheme by performing benchmark tests. Thereby we compare numerical results to analytic solutions and discuss aspects like boundary conditions, initial values, conserved quantities, and computational efficiency. On the other hand, we also comment on new qualitative insights to the Lindblad equation from its reformulation in terms of an advection-diffusion equation with source/sink terms.

quant-ph↗

arXiv2021

Bosonic fluctuations in the $( 1 + 1 )$-dimensional Gross-Neveu(-Yukawa) model at varying $μ$ and $T$ and finite $N$

Using analogies between flow equations from the Functional Renormalization Group and flow equations from (numerical) fluid dynamics we investigate the effects of bosonic fluctuations in a bosonized Gross-Neveu model -- namely the Gross-Neveu-Yukawa model. We study this model for finite numbers of fermions at varying chemical potential and temperature in the local potential approximation. Thereby we numerically demonstrate that for any finite number of fermions and as long as the temperature is non-zero, there is no $\mathbb{Z}_2$ symmetry breaking for arbitrary chemical potentials.

hep-ph↗