Abstract
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.
Highlights
Our results suggest that there is no inhomogeneous phase in the continuum limit
In this work we studied the phase diagram of the 2 + 1-dimensional GN model with chiral imbalance introduced via a chiral chemical potential μ45 using the mean-field approximation
Our lattice field theory results indicated that an inhomogeneous phase exists at finite lattice spacing a, when using a specific lattice discretization (W 2 = W 2 )
Summary
The Gross-Neveu (GN) model describes a theory of Nf fermion flavors with a quartic interaction. In recent works [25–28] it has been discussed that inhomogeneous phases might be related to so-called moat regimes, where the bosonic wave function renormalization Z is negative Such a regime has been found in an FRG study of the phase diagram of quantum chromodynamics (QCD) [29]. The existence of inhomogeneous phases was explored in the 2 + 1dimensional GN model in the mean-field approximation [31–33]. Such 2 + 1-dimensional four-fermion theories are of interest both in high energy physics [34–38] and in condensed matter physics [39–46], and to study conceptual questions, e.g., renormalizability in the 1/N expansion or in a perturbative approach [47–50]. For the remainder of this paper we exclusively consider the limit Nf → ∞
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