Concept of Contact Matrix in Dilute Quantum Systems

The diluteness of ultracold atoms leads to universal thermodynamic relations governed by contact in $s$-wave scattering. In this talk, I will show that the concept of contact can be generalized to an arbitrary partial-wave scattering. Furthermore, to have a complete description of the pairwise correlation in a general dilute quantum system, contact should be defined as a matrix. Whereas the diagonal terms of such matrix include contact of all partial wave scatterings, the off-diagonal terms characterize the coherence of the asymptotic pairwise wavefunction in the angular momentum space. Contact matrix allows physicists to access unexplored connections between short-range correlations and macroscopic quantum phenomena. I will discuss examples of applications of contact matrix in atomic quantum Hall states and superfluids with multiple order parameters.