Dissipationless dynamics of spin supersolid states in a spin-1/2 triangular antiferromagnet with impurities

Motivated by recent experimental observations of the possible spin supersolid states in triangular lattice compounds, we study the dynamical properties of various ground states in the spin-1/2 easy-axis antiferromagnetic Heisenberg model with impurities under magnetic fields using numerical methods. In both low- and high-field spin supersolid states, the gapless Goldstone mode at the $K$ points remains robust against impurities, which is related to the presence of spin superfluidity. By contrast, we find that impurities induce a splitting of the magnon bands at the same density level in the conventional magnetic state, the so-called up-up-down state. In addition, the finite superfluid stiffness probed by the twisted phase in the spin supersolid states is consistent with the excitation spectrum. We argue that this excitation spectrum with impurity provides direct evidence for the dissipationless dynamics in the spin supersolid states, which could be tested in neutron scattering experiments.