Phase diagram of the 2+1-dimensional Gross-Neveu model with chiral imbalance

In this work, the phase diagram of the $2+1$-dimensional Gross-Neveu model is investigated with baryon chemical potential as well as chiral chemical potential in the mean-field approximation. We study the theory using two lattice discretizations, which are both based on naive fermions. An inhomogeneous chiral phase is observed only for one of the two discretizations. Our results suggest that this phase disappears in the continuum limit.Comment: 9 pages, 2 figures, contains ancillary files with plot data; talk given at the 38th International Symposium on Lattice Field theory (LATTICE 2021); July 26-30 202

Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions

In this work, inhomogeneous chiral phases are studied in a variety of Four-Fermion and Yukawa models in $2+1$ dimensions at zero and non-zero temperature and chemical potentials. Employing the mean-field approximation, we do not find indications for an inhomogeneous phase in any of the studied models. We show that the homogeneous phases are stable against inhomogeneous perturbations. At zero temperature, full analytic results are presented.Comment: 10 pages, 1 figure, contains ancillary files with plot data; talk given at the 39th International Symposium on Lattice Field theory (LATTICE 2022) in Bonn; August 8-13 202

Detecting inhomogeneous chiral condensation from the bosonic two-point function in the (1+1)(1 + 1)-dimensional Gross-Neveu model in the mean-field approximation

The phase diagram of the $(1 + 1)$-dimensional Gross-Neveu model is reanalyzed for (non-)zero chemical potential and (non-)zero temperature within the mean-field approximation. By investigating the momentum dependence of the bosonic two-point function, the well-known second-order phase transition from the $\mathbb{Z}_2$ symmetric phase to the so-called inhomogeneous phase is detected. In the latter phase the chiral condensate is periodically varying in space and translational invariance is broken. This work is a proof of concept study that confirms that it is possible to correctly localize second-order phase transition lines between phases without condensation and phases of spatially inhomogeneous condensation via a stability analysis of the homogeneous phase. To complement other works relying on this technique, the stability analysis is explained in detail and its limitations and successes are discussed in context of the Gross-Neveu model. Additionally, we present explicit results for the bosonic wave-function renormalization in the mean-field approximation, which is extracted analytically from the bosonic two-point function. We find regions -- a so-called moat regime -- where the wave function renormalization is negative accompanying the inhomogeneous phase as expected.Comment: 27 pages (main text 20, appendix 7), 2 tables, 13 figures (plot data included in arXiv source file); Updated, published versio

Unterrichtung der Belegschaftsvertretung der Tochtergesellschaft im (grenzüberschreitenden) Aktienkonzern

Die Effizienz einer Belegschaftsvertretung ist – insbesondere im Konzern – maßgeblich davon abhängig, ob die Belegschaftsvertretungen hinreichend informiert sind. Die Studie untersucht die Frage, ob und welche Folgen die Verlagerung der Entscheidungsmacht von der Mutter- auf die Tochtergesellschaft für die betriebsverfassungsrechtlichen Unterrichtungsansprüche der Arbeitnehmervertretungen der Tochtergesellschaft hat. Der Autor arbeitet zunächst die im Konzernverbund auftretenden Unterrichtungskonstellationen heraus: Abgegrenzt werden die Unterrichtungsansprüche bei der Entstehung eines Konzernverbunds – insbesondere wegen des im August 2008 in Kraft getretenen Risikobegrenzungsgesetzes – von denjenigen im bestehenden Konzern. Anschließend werden die für eine Wissenszurechnung im Konzern maßgeblichen Grundsätze erarbeitet. Anhand dieser Leitlinien werden schließlich die Pflichten der Tochtergesellschaft und ihres Vorstands bei der Unterrichtung der Belegschaftsvertretungen aufgezeigt, die aus der (grenzüberschreitenden) Verlagerung der Entscheidungsmacht folgen. Besondere Aufmerksamkeit widmet der Autor dem Schutz der Betriebs- und Geschäftsgeheimnisse der Unternehmen im Konzern

Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions

In this work, inhomogeneous chiral phases are studied in a variety of Four-Fermion and Yukawa models in 2+1 dimensions at zero and non-zero temperature and chemical potentials. Employing the mean-field approximation, we do not find indications for an inhomogeneous phase in any of the studied models. We show that the homogeneous phases are stable against inhomogeneous perturbations. At zero temperature, full analytic results are presented

Inhomogeneous phases in the chirally imbalanced 2+1-dimensional Gross-Neveu model and their absence in the continuum limit

We studied the μ-μ45-T phase diagram of the 2+1-dimensional Gross-Neveu model, where μ denotes the ordinary chemical potential, μ45 the chiral chemical potential and T the temperature. We use the mean-field approximation and two different lattice regularizations with naive chiral fermions. An inhomogeneous phase at finite lattice spacing was found for one of the two regularizations. Our results suggest that there is no inhomogeneous phase in the continuum limit. We showed that a chiral chemical potential is equivalent to an isospin chemical potential. Thus, all results presented in this work can also be interpreted in the context of isospin imbalance

Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models

We show the absence of an instability of homogeneous (chiral) condensates against spatially inhomogeneous perturbations for various 2+1-dimensional four-fermion and Yukawa models. All models are studied at non-zero baryon chemical potential, while some of them are also subjected to chiral and isospin chemical potential. The considered theories contain up to 16 Lorentz-(pseudo)scalar fermionic interaction channels. We prove the stability of homogeneous condensates by analyzing the bosonic two-point function, which can be expressed in a purely analytical form at zero temperature. Our analysis is presented in a general manner for all of the different discussed models. We argue that the absence of an inhomogeneous chiral phase (where the chiral condensate is spatially non-uniform) follows from this lack of instability. Furthermore, the existence of a moat regime, where the bosonic wave function renormalization is negative, in these models is ruled out.Comment: 26 pages (main text 15, appendix 11), 3 tables, 1 figure (plot script for reproduction of the data included in arXiv source file

Inhomogeneous phases in the 3+1-dimensional Nambu-Jona-Lasinio model and their dependence on the regularization scheme

In this work we study the 3+1-dimensional Nambu-Jona-Lasinio (NJL) model in the mean field-approximation. We carry out calculations using five different regularization schemes (two continuum and three lattice regularization schemes) with particular focus on inhomogeneous phases and condensates. The regularization schemes lead to drastically different inhomogeneous regions. We provide evidence that inhomogeneous condensates appear for all regularization schemes almost exclusively at values of the chemical potential and with wave numbers, which are of the order of or even larger than the corresponding regulators. This can be interpreted as indication that inhomogeneous phases in the 3+1-dimensional NJL model are rather artifacts of the regularization and not a consequence of the NJL Lagrangian and its symmetries