Fluctuations and correlations of quark spin in hot and dense QCD matter

In this work, we examine the impact of QCD phase transitions on the quark spin fluctuations and correlations. We propose the quark-antiquark correlation, which relates to the vector meson spin alignment and the $\mathrm{\Lambda }-\bar{\mathrm{\Lambda }}$ correlation, can be used as a novel probe of the critical end point (CEP) in the QCD phase diagram. Using the Nambu-Jona-Lanisio model, we qualitatively study the properties of quark-antiquark spin correlations. Our findings reveal a peak structure near the CEP of the chiral phase transition, which may serve as an experimental signature of the CEP and account for the non-monotonic behavior of $\phi$ meson alignment at low collision energies observed recently in experiments.