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

Stefano Carignano,Marco Schramm,Michael Buballa

doi:10.1103/physrevd.98.014033

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.

Highlights

The phase structure of QCD at high densities and intermediate temperatures is expected to be extremely rich
A fascinating scenario suggested by explicit model calculations revolves around the formation of an inhomogeneous “island”, characterized by the presence of crystalline chiral condensates, which can appear in the region where the first-order chiral phase transition is expected to take place
We investigated the effects of vector interactions on inhomogeneous chiral symmetry breaking within the NJL model, expanding on previous studies where the vector condensate was approximated by its spatial average [12]

Summary

INTRODUCTION

The phase structure of QCD at high densities and intermediate temperatures is expected to be extremely rich. In order to be able to use known analytical expressions for the eigenvalue spectrum of the Dirac Hamiltonian in the presence of certain crystalline backgrounds, instead of considering a spatially modulated density, the vector mean field was approximated by its spatial average. Case for modulations like the RKC [12] or even a simple sinusoidal Ansatz For these cases, a repulsive vector interaction might generate an additional energy cost for the formation of a spatially modulated quark density, possibly influencing the competition between different crystalline phases and altering the resulting phase structure of the model.

MODEL AND BASIC FORMALISM

GINZBURG-LANDAU EXPANSION

NUMERICAL DIAGONALIZATION BEYOND THE AVERAGE-DENSITY APPROXIMATION

CONCLUSION