Projective symmetry group analysis of symmetric U(1) and Z₂ multipolar quantum spin liquids on the pyrochlore lattice

Multipolar pyrochlore rare-earths magnets form an interesting class of quantum spin liquids (QSLs) candidates. The intrinsic relation between their pseudo-spin degree of freedom and the local crystalline environment may lead to enhanced quantum fluctuations, disorder-promoted QSLs, and novel detection schemes. In this work, we extend the previous projective symmetry group (PSG) classification of Z₂ QSLs on the pyrochlore lattice for bosonic spinons by Liu, Halàsz, and Balents [Phys. Rev. B 100, 075125 (2019)] to multipolar QSLs and further determine all U(1) PSG classes.