Universal relations and Tan contact matrix for 1D spinor quantum gases

The Tan contact and associated Tan relations, such as the tail of the momentum distribution, have been previously studied for a few kinds of spinor quantum gases, such as spin-zero/half fermions, bosons, SU(N) symmetric cases or multicomponent gases. Inspired by our previous work on interacting spinor quantum gases with arbitrary spins, we present results of our investigation of the Tan contact matrix and its connection to the large momentum tail for arbitrary spin cases with spin-dependent interactions at arbitrary strengths. We further discuss the connection of the Tan contact matrix to two body density matrices, energetics and other universal relations.