Nematic and supernematic phases in kagome quantum antiferromagnets under the influence of a magnetic field

Optimizing translationally invariant infinite-projected entangled pair states, we investigate the spin-2 Affleck-Kennedy-Lieb-Tasaki and spin-1 Heisenberg models on the kagome lattice as a function of magnetic field. We found that the magnetization curves offer a wide variety of compressible and incompressible phases. Incompressible nematic phases breaking the lattice C-3 rotation, for which we propose simple qualitative pictures, give rise to magnetization plateaus at reduced magnetization m(z) = 5/6 and 1/3 for spin-2 and -1, respectively, in addition to the mz = 0 plateaus characteristic of zero-field gapped spin liquids. Moving away from the plateaus, we observe a rich variety of compressible superfluid nematic, named "supernematic," phases breaking spontaneously both point group and spin-U(1) symmetries, as well as a superfluid phase preserving lattice symmetries. We also identify the nature, continuous or first order, of the various phase transitions. Possible connections to experimental spin-1 systems are discussed.