Dynamical signatures of Hardcore-Boson Supersolid on the Triangular Lattice

We investigate the dynamical signatures of the supersolid phase in the triangular-lattice hardcore Bose-Hubbard model via large-scale quantum Monte Carlo simulations and linear spin-wave theory. We reveal a distinct momentum-space separation in the spectral weights. The transverse spectrum shows gapless Goldstone modes at the $Γ$ and $K$ points, while the longitudinal spectrum features a gapless mode at $K$ and a roton-like minimum at $M$. Directly in the imaginary-time domain, the supersolid is unambiguously characterized by the coexistence of transverse spectral lines at $Γ$ and $K$. Furthermore, we show that strong quantum fluctuations induce a breakdown of the sharp quasiparticle picture, leading to asymmetric line shapes and broad continua. Our work establishes the definitive dynamical signatures of the hardcore-boson supersolid, providing key insights into analogous spin supersolids in triangular quantum magnets.