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In this work, we study a slave-rotor mean-field theory of an extended Hubbardmodel, applicable to transition metal dichalcogenide moir\'e systems, thatcaptures both the formation of Wigner crystals as well as exotic spin states ontop of these charge backgrounds. Phase diagrams are mapped out for differentchoices of long-range Coulomb repulsion strength, reproducing severalexperimentally found Wigner crystal states. Assuming unbroken time reversalsymmetry, we find several spin liquid states as well as dimer states atfractional fillings. While spin dimer states are always found to have thelowest mean field energy, several spin liquid states are energeticallycompetitive and may be stabilized by including gauge fluctuations or furtherinteraction terms. We further discuss possible experimental signatures of thesestates pertinent to two-dimensional moir\'e heterostructures.

Mott insulators in moir\'e transition metal dichalcogenides at fractional fillings: Slave-rotor mean-field theory