Axial-Vector and Tensor Spin Polarization and Chiral Restoration in Quark Matter

We study spontaneous spin-polarizations of quark matter with flavour $SU(2)$ symmetry at zero temperature in the NJL model. In a relativistic framework, there are two types of the spin-spin interactions: axial-vector (AV) and tensor (T), which accordingly give rise to different types of spin-polarized materials. When the spin-spin interaction is sufficiently strong, the spin-polarized phase emerges within a specific density region. As the spin-spin interaction becomes stronger, this phase extends over higher density region beyond the critical density of chiral restoration in normal quark matter. We show that the spin-polarized phase leads to another kind of the spontaneous chiral symmetry breaking phase.