Gapless fracton quantum spin liquid and emergent photons in a 2D spin-1 model

Gapless fracton quantum spin liquids are exotic phases of matter described by higher-rank U(1) gauge theories, which host gapped and immobile fracton matter excitations as well as gapless photons. Despite well-known field theories, no spin models beyond purely classical systems have been identified to realize these phases. Using error-controlled Green function Monte Carlo, here we investigate a square lattice spin-1 model that shows precise signatures of a fracton quantum spin liquid without indications of conventional ordering. Specifically, the magnetic response exhibits characteristic patterns of suppressed pinch points that accurately match the prediction of a rank-2 U(1) field theory and reveals the existence of emergent photon excitations in 2+1 spacetime dimensions. Remarkably, this type of fracton quantum spin liquid is not only identified in the system's ground state but also in generic low-energy sectors of a strongly fragmented Hilbert space.