Spin liquid in twisted homobilayers of group-VI dichalcogenides

Twisted transition metal dichalcogenide (TMD) homobilayers have recently emerged as a powerful platform for studying correlated insulating states. In the strongly limit, we construct an effective spin Hamiltonian on honeycomb lattice that includes Heisenberg interaction and nonsymmetric interactions such Dzyaloshinskii-Moriya Kane-Mele coupling Mott-insulating phase at half-filling. For twisted TMD homobilayers, spin-orbit in Hubbard model, which is expected to induce antisymmetric exchange couplings Hamiltonian, highly tunable experimentally accessible quantity can be tuned by applied electric field. this study, investigate classical quantum diagrams of using analytical numerical methods. We show model exhibits rich diagram including antiferromagnetic (AFM) phase, planar spiral ordered with high degeneracy, $z$-AFM noncoplanar noncollinear 120$^{\circ}$-AFM phase. treatment, calculate low-energy magnon excitation spectrum, ground state energy, static structure factor linear spin-wave theory density matrix renormalization group methods compose Hamiltonian. Beyond interaction, find existence these responsible liquid, $z$-AFM, noncoplanar, 120$^{\circ}$ phases. therefore, offer platforms realizing phases matter 120$^{\circ}$, resulting from coupling.