Detecting inhomogeneous chiral condensation from the bosonic two-point function in the (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 Z2 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.

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Metadaten
Author:Adrian KoenigsteinORCiDGND, Laurin PannulloORCiDGND, Stefan RechenbergerGND, Martin J. SteilORCiD, Marc WinstelORCiD
URN:urn:nbn:de:hebis:30:3-797226
URL:https://arxiv.org/abs/2112.07024v1
DOI:https://doi.org/10.48550/arXiv.2112.07024
ArXiv Id:http://arxiv.org/abs/2112.07024v1
Parent Title (German):arXiv
Publisher:arXiv
Document Type:Preprint
Language:English
Date of Publication (online):2021/12/13
Date of first Publication:2021/12/13
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2024/02/26
Tag:Gross-Neveu model; inhomogeneous phases; mean-field; moat regime; phase diagram; stability analysis; two-point function; wave-function renormalization
Issue:2112.07024 Version 1
Edition:Version 1
Page Number:25
HeBIS-PPN:516880888
Institutes:Physik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Sammlungen:Universitätspublikationen
Licence (German):License LogoCreative Commons - Namensnennung 4.0