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Random matrix model at nonzero chemical potentials with anomaly effects

Phase diagram of the chiral random matrix model with U(1)A breaking term is studied with the quark chemical potentials varied independently at zero temperature, by taking the chiral and meson condensates as the order parameters. Although, without the U(1)A breaking term, chiral transition of each flavor can happen separately responding to its chemical potential, the U(1)A breaking terms mix the chiral condensates and correlate the phase transitions. In the three flavor case, we find that there are mixings between the meson and chiral condensates due to the U(1)A anomaly, which makes the meson condensed phase more stable. Increasing the hypercharge chemical potential ($μ_Y$) with the isospin and quark chemical potentials ($μ_I$, $μ_q$) kept small, we observe that the kaon condensed phase becomes the ground state and at the larger $μ_Y$ the pion condense phase appears unexpectedly, which is caused by the competition between the chiral restoration and the meson condensation. The similar happens when $μ_Y$ and $μ_I$ are exchanged, and the kaon condensed phase becomes the ground state at larger $μ_I$ below the full chiral restoration.