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Phenomenological approach to hyperkagome spin liquid: gauge fields and spinons without slave particles

A number of experiments on the hyperkagome iridate, Na$_4$Ir$_3$O$_8$, suggest existence of a gapless quantum spin liquid state at low temperature. Circumventing the slave particle approach commonly used in theoretical analyses of frustrated magnets, we provide a more intuitive, albeit more phenomenological, construction of a quantum spin liquid state for the hyperkagome Heisenberg model. An effective monomer-dimer model on the hyperkagome lattice is proposed a la Hao and Tchernyshyov's approach cultivated from the Husimi cactus model. Employing an arrow representation for the monomer-dimer model, we obtain a compact $U(1)$ gauge theory with a finite density of Fermionic spinons on the hyperoctagon lattice. The resulting theory and its mean field treatments lead to remarkable agreement with previous slave-particle construction of a quantum spin liquid state on the hyperkagome lattice. Our results offer novel insights on theoretical understanding of the emergence of spinon Fermi surfaces and useful predictions for future experiments.