  Motivated by recent experiments on the quantum-spin-liquid candidate material
LiZn2Mo3O8, we study a single-band extended Hubbard model on an anisotropic
Kagome lattice with the 1/6 electron filling. Due to the partial filling of the
lattice, the inter-site repulsive interaction is necessary to generate Mott
insulators, where electrons are localized in clusters, rather than at lattice
sites. It is shown that these cluster Mott insulators are generally U(1)
quantum spin liquids with spinon Fermi surfaces. The nature of charge
excitations in cluster Mott insulators can be quite different from conventional
Mott insulator and we show that there exists a novel cluster Mott insulator
where charge fluctuations around the hexagonal cluster induce a plaquette
charge order (PCO). The spinon excitation spectrum in this spin-liquid cluster
Mott insulator is reconstructed due to the PCO so that only 1/3 of the total
spinon excitations are magnetically active. Based on these results, we propose
that the two Curie-Weiss regimes of the spin susceptibility in LiZn2Mo3O8 may
be explained by finite-temperature properties of the cluster Mott insulator
with the PCO as well as fractionalized spinon excitations. Existing and
possible future experiments on LiZn2Mo3O8, and other Mo-based cluster magnets
are discussed in light of these theoretical predictions.
