In the strong easy-axis limit, the triangular XXZ model reduces to a honeycomb-lattice boson model with nearest-neighbour repulsion, whose one-loop spectrum yields a sqrt(V) pseudo-Goldstone gap and no roton minimum.
Modified large-$N$ approach to gapless spin liquids, magnetic orders, and dynamics: Application to triangular lattice antiferromagnets
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abstract
Recent work has shown that the triangular lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg and XXZ antiferromagnets may exhibit coplanar or supersolid orders proximate to a gapless Dirac spin liquid phase. We explore a distinct $SU(2N)\!\!\times\!\!SU(M)$ fermionic parton approach, complemented by variational Monte Carlo calculations for the spin-$1/2$ 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$_2$.
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Non-linear spin wave theory in the strong easy-axis limit of the triangular XXZ model
In the strong easy-axis limit, the triangular XXZ model reduces to a honeycomb-lattice boson model with nearest-neighbour repulsion, whose one-loop spectrum yields a sqrt(V) pseudo-Goldstone gap and no roton minimum.