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

Abstract

We study the $\mu$-${\mu }_{45}$-$T$ phase diagram of the $2+1$-dimensional Gross-Neveu model, where $\mu$ denotes the ordinary chemical potential, ${\mu }_{45}$ 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 is found for one of the two regularizations. Our results suggest that there is no inhomogeneous phase in the continuum limit. We show 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.

18 pages, 7 figures, 1 table; plot data provided in arXiv source; version as published in symmetry

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Cited by in corpus (8)

• Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models
• Regularization effects in the Nambu-Jona-Lasinio model: Strong scheme dependence of inhomogeneous phases and persistence of the moat regime
• Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
• Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions $1\le d<3$. II. Nonzero temperature and chemical potential
• Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions
• Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions $1\le d<3$
• Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density
• Revisiting the spatially inhomogeneous condensates in the $(1+1)$-dimensional chiral Gross-Neveu model via the bosonic two-point function in the infinite-$N$ limit