Abstract In this chapter we review the phenomenology of K mesons, or kaons, and the possibility of Bell-inequality violation in systems of K-meson pairs. To this end we first study their properties and features: strangeness represented by the strange quark, the violation of the charge-conjugation parity (CP) symmetry, strangeness oscillation, and regeneration. These interesting phenomena emerge from the fact that the strangeness eigenstates, CP eigenstates, and mass eigenstates are not the same, as well as from the interplay of the strangeness-conserving and CP-conserving strong interaction and the weak interaction which violates these conservation rules. We then examine the quasi-spin analogy of K mesons and the correlation functions for entangled K-meson pairs. After concluding that the physical measurements possible for K-mesons do not allow a direct violation of Bell inequalities such as the Uchiyama-Bell inequality we identify the CP violation as an indirect violation of Bell inequalities.
We study a two-flavor fermion model where each of the flavors form a Sachdev-Ye-Kitaev (SYK) system with arbitrary
q-body interactions. The crucial new element is an all-to-all
r-body interaction between the two flavors. At high temperatures, the model shows a strange metal phase where both flavors are gapless, similar to the usual single-flavor SYK model. Upon reducing temperature, the coupled system undergoes transitions to previously unseen phases in the SYK framework---first, a strange half-metal phase where one flavor remains a strange metal while the other is gapped, and second, an insulating phase of the Mott kind where both flavors are gapped. At a fixed low temperature, we obtain transitions between these phases by tuning the relative fraction of sites for each flavor. We discuss the physics of these phases and the nature of transitions between them. This work provides an example of an instability of the strange metal with potential to provide new routes to study strongly correlated systems through the rich physics contained in SYK-like models.