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

TL;DR

This paper demonstrates that in certain 2+1-dimensional fermionic models, homogeneous chiral condensates are stable and do not develop inhomogeneous phases, ruling out the existence of spatially non-uniform chiral condensates at non-zero chemical potential.

Contribution

It provides a general analytical proof of the absence of inhomogeneous chiral phases in various 2+1D four-fermion and Yukawa models at finite chemical potential.

Findings

Homogeneous condensates are stable against inhomogeneous perturbations.

No inhomogeneous chiral phase exists in the studied models.

The moat regime with negative wave function renormalization is ruled out.

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.