Random matrix model at nonzero chemical potentials with anomaly effects

TL;DR

This paper investigates the phase diagram of a chiral random matrix model with U(1)A anomaly effects at nonzero chemical potentials, revealing how anomaly-induced mixing influences phase transitions and the stability of meson condensed phases.

Contribution

It introduces a detailed analysis of the impact of U(1)A anomaly terms on phase transitions in a three-flavor chiral random matrix model with independent chemical potentials.

Findings

U(1)A breaking terms cause mixing between chiral and meson condensates.

Kaon condensed phase becomes the ground state at certain chemical potentials.

Unexpected pion condensation occurs at larger hypercharge chemical potential.

Abstract

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 ($\mu_Y$) with the isospin and quark chemical potentials ($\mu_I$, $\mu_q$) kept small, we observe that the kaon condensed phase becomes the ground state and at the larger $\mu_Y$ the pion condense phase appears unexpectedly, which is caused by the competition between the chiral restoration and the meson condensation. The similar happens when $\mu_Y$ and $\mu_I$ are exchanged, and the kaon condensed phase becomes the ground state at larger $\mu_I$ below the full chiral restoration.