From Hadrons to Quarks in Dense Matter

In this presentation, we argue a crossover transition from baryonic matter to quark matter, triggered by the saturation of quark states in dense matter ({\it quark saturation}). Unlike traditional first-order hadron-to-quark phase transitions, this crossover transition is characterized by a rapid increase in pressure relative to energy density, resulting in a distinct peak in the speed of sound, consistent with recent observational constraints from neutron star physics. The quark saturation can occur at a few times nuclear saturation density --- notably lower than the density at which the baryon cores of $\sim 0.5$--$0.8$ fm spatially overlap.As a concrete realization of such a crossover, we consider quarkyonic matter scenario,providing a unified description across both baryonic and quark domains. We introduce the {\it IdylliQ} model---an ideal representation of quarkyonic matter---to explicitly delineate the relationship between baryon and quark occupation probabilities. Furthermore, we illustrate how the stiffening of the equation of state is driven by the Pauli exclusion principle acting on quark states. The model is extended to charge-neutral matter including hyperons, revealing that statistical constraints at the quark level induce an effective repulsion among different baryon species. This mechanism naturally mitigates the {\it hyperon softening problem} in the context of massive neutron stars.