Single-impurity polarons in hard-core lattice bosons at low and intermediate fillings

Abstract

We investigate a single mobile impurity in a two-dimensional hard-core Bose--Hubbard bath at low and intermediate fillings and determine how polaronic dressing evolves with bath filling for impurity--bath couplings ranging from weak to strong and ultimately to the two-component hard-core limit. Using large-scale, sign-problem-free worm-algorithm quantum Monte Carlo simulations, we extract momentum-space quasiparticle properties from the impurity Green's function and resolve the accompanying real-space bath rearrangement from an imaginary-time-averaged impurity-centered correlator. We also vary the impurity hopping $t_{\rm imp}$ to assess how reduced mobility modifies dressing in the strong-coupling regime. For the fillings accessible at each coupling, the impurity remains a dressed quasiparticle whose ground-state energy, effective mass, and residue vary smoothly with filling $n_{\rm b}$. In real space, increasing $n_{\rm b}$ strengthens the short-range depletion while shifting the dominant response toward the impurity. In the two-component hard-core limit $U_{\rm ib}/t_{\rm b}\!\to\!\infty$, the large-distance recovery of the cumulative density deformation exhibits only weak filling dependence over the range considered here, whereas short-range core indicators continue to evolve. Our results quantitatively characterize strongly dressed polarons in a correlated, compressible lattice bath and resolve how filling and impurity mobility modify the near-core response and spatial extent of the dressing cloud.