Mobile impurity coupled to correlated lattice bosons

TL;DR

This paper studies how a single impurity's coherence and spatial dressing change in a 2D Bose-Hubbard model when it couples attractively to the bath, revealing a crossover from mobile to self-trapped states influenced by the bath's phase.

Contribution

It provides a detailed quantum Monte Carlo analysis of impurity behavior in correlated lattice bosons, highlighting the interaction-driven winding-collapse crossover and impurity undressing across the superfluid-Mott insulator transition.

Findings

Winding-collapse self-trapping crossover in superfluid baths.

Suppressed density rearrangements and collapse of dressing cloud in Mott insulators.

Impurity transitions from a mobile polaron to a nearly free defect across the SF-MI transition.

Abstract

We investigate how the coherence and spatial dressing of a single impurity evolve in the two-dimensional Bose-Hubbard model when the impurity couples attractively to the bath. Using large-scale, sign-problem-free worm-algorithm quantum Monte Carlo, we measure the impurity winding, bath superfluid response and compressibility, and impurity-bath density correlations. In a compressible superfluid bath ($U_{\mathrm{b}}/t=13.3$), strengthening attraction drives an interaction-controlled \emph{winding-collapse self-trapping crossover}: a mobile light polaron evolves continuously into a heavy polaron and ultimately into a bound cluster with vanishing winding, while the bath remains globally superfluid. In incompressible Mott-insulating baths, by contrast, extended density rearrangements are suppressed and the dressing cloud collapses; we compare the resulting short-range deformation patterns for both attractive and repulsive couplings. Across the SF-MI transition at fixed moderate attraction ($U_{\mathrm{ib}}/t=-8.0$), the impurity crosses over from a mobile polaron with an extended deformation cloud to a nearly free defect with minimal dressing in the Mott background; for this coupling it does not lock into a fully self-trapped defect even deep in the insulator. Together with our companion Letter [Impurity Self-Trapping in Lattice Bose systems] on repulsive couplings, these results provide a unified microscopic picture of impurity self-trapping in correlated lattice bosons, connecting interaction-driven winding collapse in the superfluid to compressibility-controlled undressing across the SF-MI transition.