The single-flavor excluded-volume model based on the effective size of baryons reproduces the hard-soft density evolution of the equation of state (EoS) required by the recent studies of GW170817. This phenomenological model basically realizes the concept of quarkyonic matter which is introduced from large-$N_c$ gauge theory for dense matter. Enhanced nucleon interactions and dynamically generated quark degrees of freedom can reproduce the hard-soft evolution of the EoS. In this paper, we extend the excluded-volume model to a three-flavor system by considering electromagnetic charge and possible weak equilibrium in order to obtain a proper description for the hard-soft behavior of the EoS inferred from the gravitational waves observations.

We show how a scheme of rewriting a divergent momentum integral can conciliate results obtained with the Nambu–Jona-Lasinio model and recent lattice results for the chiral transition in the presence of a chiral imbalance in quark matter. Purely vacuum contributions are separated from medium-dependent regularized momentum integrals in such a way that one is left with ultraviolet divergent momentum integrals that depend on vacuum quantities only. The scheme is applicable to other commonly used effective models to study quark matter with a chiral imbalance, it allows us to identify the source of their difficulties in reproducing the qualitative features of lattice results, and enhances their predictability and uses in other applications.

We extend the excluded-volume model of isospin symmetric two-flavor dense quarkyonic matter [ Phys. Rev. C 101, 035201 (2020)] including strange particles and address its implications for neutron stars. The effective sizes of baryons are defined from the diverging hard-core potentials in the short interdistance regime. Around the hard-core density, the repulsive core between baryons at short distances leads to a saturation in the number density of baryons and generates perturbative quarks from the lower phase space, which leads to the shell-like distribution of baryons by the Pauli exclusion principle. The strange-quark Fermi sea always appears at high densities but the $\mathrm{\Lambda }$ hyperon shell only appears when the effective size of the $\mathrm{\Lambda }$ hyperon is smaller than the effective size of nucleons. We find that the pressure of strange quarkyonic matter can be large enough to support neutron stars with two times solar mass and can have a large sound speed, $c_s^2\simeq 0.7$. The fraction of the baryon number carried by perturbative quarks is about 30% at the inner core of most massive neutron stars.

The BEC-BCS crossover for a Nambu–Jona-Lasinio (NJL) model with diquark interactions is studied in the presence of an external magnetic field. Particular attention is paid to different regularization schemes used in the literature. A thorough comparison of results is performed for the case of a cold and magnetized two-color NJL model. According to our results, the critical chemical potential for the BEC transition exhibits a clear inverse magnetic catalysis effect for magnetic fields in the range $1\lesssim eB/m_{\pi }^2\lesssim 20$. As for the BEC-BCS crossover, the corresponding critical chemical potential is very weakly sensitive to magnetic fields up to $eB\sim 9m_{\pi }^2$, showing a much smaller inverse magnetic catalysis as compared to the BEC transition, and displays a strong magnetic catalysis from this point on.

We compute the QCD equation of state for zero temperature and finite isospin density within the Nambu–Jona-Lasinio model in the mean field approximation, motivated by the recently obtained lattice QCD results for a new class of compact stars: pion stars. We have considered both the commonly used traditional cutoff regularization scheme and the medium separation scheme, where in the latter purely vacuum contributions are separated in such a way that one is left with ultraviolet divergent momentum integrals depending only on vacuum quantities. We have also compared our results with the recent results from lattice QCD and chiral perturbation theory.

Symmetry restoration in a theory of a self-interacting charged scalar field at finite temperature and in the presence of an external magnetic field is examined. The effective potential is evaluated nonperturbatively in the context of the optimized perturbation theory method. It is explicitly shown that in all ranges of the magnetic field, from weak to large fields, the phase transition is second order and that the critical temperature increases with the magnetic field. In addition, we present an efficient way to deal with the sum over the Landau levels, which is of interest especially in the case of working with weak magnetic fields.