Modified large-$N$ approach to gapless spin liquids, magnetic orders, and dynamics: Application to triangular lattice antiferromagnets

Recent work has shown that the triangular lattice spin-$1\mathrm{/}2$ $J_1$-$J_2$ Heisenberg and XXZ antiferromagnets may exhibit coplanar or supersolid orders proximate to a gapless Dirac spin liquid phase. We explore a distinct $SU(2N)\text{\hspace{0.17em}⁣}\text{\hspace{0.17em}⁣}\times \text{\hspace{0.17em}⁣}\text{\hspace{0.17em}⁣}SU(M)$ fermionic parton approach, complemented by variational Monte Carlo calculations for the spin-$1\mathrm{/}2$ model, to study the phase diagram of these models. We also calculate their dynamical spin response including parton interactions within a random phase approximation, and discuss implications for neutron scattering on triangular lattice cobaltates Ba${}_3$CoSb${}_2$O${}_9$, Na${}_2$BaCo(PO${}_4$)${}_2$, K${}_2$Co(SeO${}_3$)${}_2$, Rb${}_2$Co(SeO${}_3$)${}_2$, and Yb-based magnet KYbSe${}_2$.