Quasicrystals in QCD

We study the ground state of the low energy dense QCD with the assumption of chiral condensates of quarks. Under an external magnetic field, mesons could form soliton lattices via the chiral anomaly. For such scenarios, we present a unified description of pions and $\eta$ meson with a $U(2)$ field in the framework of the chiral perturbation theory. Our result shows the ground state is a mixture of the magnetized domain walls formed by neutral pion $\pi^0$ and $\eta$ meson when they coexist. The winding number of the ground state would alter according to the strength of the magnetic field. When the magnetic field is strong or the chemical potential is large, the proportion of the mixture is determined by the decay constants and the contributions to the anomalous action of $\pi^0$ and $\eta$ meson. The resulting configuration is either a mixed soliton lattice or a quasicrystal which could be dubbed a ``chiral soliton quasicrystal''.