Influence of vector interactions on the favored shape of inhomogeneous chiral condensates

TL;DR

This study investigates how vector interactions influence the preferred shape of inhomogeneous chiral condensates in the NJL model, revealing that increased vector coupling favors chiral density wave modulations over sinusoidal ones.

Contribution

It demonstrates that considering a spatially modulated vector mean-field alters the favored inhomogeneous chiral condensate shape, a novel insight in the NJL model analysis.

Findings

Chiral density wave becomes favored with higher vector coupling.

Both Ginzburg-Landau and numerical methods confirm the shape transition.

Vector interactions significantly impact inhomogeneous phase structures.

Abstract

We update a previous study of the effects of vector interactions in the Nambu--Jona-Lasinio model on the formation of inhomogeneous chiral symmetry breaking condensates. In particular, by properly considering a spatially modulated vector mean-field associated with the quark number density of the system we show that, as the value of the vector coupling increases, a chiral density wave modulation can become thermodynamically favored over a real sinusoidal modulation. This behavior is found both via a Ginzburg-Landau analysis close to the Lifshitz point, as well as with a full numerical diagonalization of the mean-field Dirac Hamiltonian at vanishing temperature.