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

Abstract

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.

26 pages (main text 15, appendix 11), 3 tables, 1 figure (plot script for reproduction of the data included in arXiv source file), v2: Extended the discussion section, no changes in the results. Version as accepted for publication in Physical Review D

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• 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
• Dissecting the moat regime at low energies I: Renormalization and the phase structure