Valence bond solids and hidden order phases in a pyrochlore U(1) quantum spin liquid

Antiferromagnetic spin-1/2 system on a pyrochlore lattice has been extensively studied as a host of the exotic phase of matter, U(1) quantum spin liquid (QSL). In a low-energy sector, the spin degrees of freedom are mapped to the emergent U(1) gauge fields and fractionalized excitations. As the kinematics of the fractionalized excitations dominates the system, the emergent gauge structure is broken and the QSL encounters the magnetic instability. Beyond the U(1) QSL and the conventional orderings, the realization of unconventional phases such as the spin nematic, multiple order etc., in frustrated magnet opens an interesting question. Here, we study the pyrochlore XXZ model with farther and competing exchange interactions. Analyzing the effective spinon actions, we schematically depict the richer phase diagram exhibiting the valence bond solids, spin nematic, and inversion breaking hidden orders.