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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References in corpus (8)

• Exact evolution equation for the effective potential
• Color superconductivity in dense quark matter
• Inhomogeneous chiral condensates
• Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model
• Inhomogeneous phases in the quark-meson model with vacuum fluctuations
• How transverse thermal fluctuations disorder a condensate of chiral spirals into a quantum spin liquid
• Comparison of the non-uniform chiral and 2SC phases at finite temperatures and densities
• Phase diagram of the non-uniform chiral condensate in different regularization schemes at T=0

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• Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions $1\le d<3$
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• Exact Wigner function for chiral spirals