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We present exact numerical data for the lowest-energy momentum eigenstates(yrast states) of a repulsive spin impurity in a one-dimensional Bose gas usingfull configuration interaction quantum Monte Carlo (FCIQMC). As a stochasticextension to exact diagonalization it is well suited for the study of yraststates of a lattice-renormalized model for a quantum gas. Yrast states carryvaluable information about the dynamic properties of slow-moving mobileimpurities immersed in a many-body system. Based on the energies and the firstand second order correlation functions of yrast states, we identify differentdynamical regimes and the transitions between them: The polaron regime, wherethe impurity's motion is affected by the Bose gas through a renormalizedeffective mass; a regime of a gray soliton that is weakly correlated with astationary impurity, and the depleton regime, where the impurity occupies adark or gray soliton. Extracting the depleton effective mass reveals a superheavy regime where the magnitude of the (negative) depleton mass exceeds themass of the finite Bose gas.

Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity