A simple effective model for the intermediate-density regime is constructed from the high-density effective theory of quantum chromodynamics (QCD). In the effective model, under a renormalization group (RG) scaling toward low momenta, the original QCD interactions lead to four-quark contact interactions for the relevant quark and hole modes around the Fermi surface. The contact interaction in the scalar channel can be traced back to zero-sound-type collinear quark scattering near the Fermi surface in an instanton background. The quark and hole states in opposite directions of a given Fermi velocity form the collective scalar bosonic mode $\sigma$. The magnitude of $\sigma$ is investigated via the nonperturbative functional renormalization group evolution of the effective average action from the ultraviolet to the infrared (IR). In the mean-background-field approximation for $\sigma$, nontrivial minima ($\overline{\sigma }\ne 0$) are found in the IR limit of the effective average action. A nonvanishing $\overline{\sigma }$ corresponds to condensation of quark and hole states in opposite directions of a given Fermi velocity, in a thin shell-like structure in momentum space around the Fermi surface. This looks similar to the shell-like baryon distribution in momentum space assumed in the quarkyonic-matter concept. However, when including a dynamic bosonic $\sigma$ mode in the RG flow, we find that its diffusive nature destroys the quark-hole condensate, i.e., the IR potential does not show any minima beyond the trivial one.

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• Effective field theory
• Exotic phases of matter
• Models based on symmetries
• Nuclear matter
• Phase diagrams
• Phase transitions
• QCD in nuclear reactions
• QCD phase transitions
• Quantum chromodynamics
• Quantum phase transitions
• Quark matter
• Renormalization group
• Thermal & statistical models