This three-year, $485,084 National Science Foundation Division of Materials Research Project Grant will support research into emergent quantum phenomena through muon spin relaxation, neutron scattering, and scanning tunneling microscopy experiments. Led by researchers at Columbia University, the project aims to elucidate charge-spin interplays in unconventional superconductors and Mott transition systems through measurements of superfluid density, dynamic spin fluctuations, order parameters, and local spin correlations. Findings will be interpreted using the Principal Investigator's phenomenology on unconventional superconductivity developed since 1989. Additional goals include testing hypotheses regarding highly entangled spin-charge gaps in Mott transition materials, field-induced changes in cuprate superconductors, and the effects of topology in skyrmion and topological systems. Outreach activities like workshops and lectures will engage students and early career researchers. This award falls under the NSF Mathematical and Physical Sciences program to advance the progress of mathematical and physical sciences.