Competition of inhomogeneous chiral phases and two-flavor color superconductivity in the NJL model

Abstract

We study the phase structure of the two-flavor Nambu--Jona-Lasinio (NJL) model in the chiral limit, extending a previous study of the competition of an inhomogeneous chiral phase and a two-flavor color-superconducting (2SC) phase [1, 2]. There, an analytic expression for the dispersion relations for quasiparticle excitations in the presence of both a particular inhomogeneous chiral condensate, the so-called chiral density wave (CDW), and a homogeneous 2SC condensate was found. In this work we show how to determine the dispersion relations for arbitrary modulations of the chiral condensate in the presence of a homogeneous 2SC condensate, if the dispersion relations in the absence of color superconductivity are known. In our calculations, we employ two different Ansätze for the inhomogeneous chiral condensate, the CDW as well as the real-kink crystal (RKC). Depending on the value of the diquark coupling we find a region of the phase diagram where the inhomogeneous chiral and the 2SC condensates coexist, confirming results of Refs. [1, 2]. Decreasing the diquark coupling favors the inhomogeneous phase over the coexistence phase. On the other hand, increasing the diquark coupling leads to a larger 2SC phase, while the inhomogeneous chiral and the coexistence phases become smaller. In agreement with previous studies the RKC Ansatz is energetically preferred over the CDW Ansatz. Both Ansätze lead to a qualitatively similar phase diagram, however the coexistence phase is smaller for the RKC Ansatz.

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• Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models
• Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions $1\le d<3$
• Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions
• Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density
• Quantum fluctuation in an inhomogeneous background and its influence on the phase transition in a finite volume system
• Dual chiral density wave induced oscillating Casimir effect
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation
• Quantum fluctuation energies over a spatially inhomogeneous field background in a chiral soliton model
• Exact Wigner function for chiral spirals