  We present exact numerical data for the lowest-energy momentum eigenstates
(yrast states) of a repulsive spin impurity in a one-dimensional Bose gas using
full configuration interaction quantum Monte Carlo (FCIQMC). As a stochastic
extension to exact diagonalization it is well suited for the study of yrast
states of a lattice-renormalized model for a quantum gas. Yrast states carry
valuable information about the dynamic properties of slow-moving mobile
impurities immersed in a many-body system. Based on the energies and the first
and second order correlation functions of yrast states, we identify different
dynamical regimes and the transitions between them: The polaron regime, where
the impurity's motion is affected by the Bose gas through a renormalized
effective mass; a regime of a gray soliton that is weakly correlated with a
stationary impurity, and the depleton regime, where the impurity occupies a
dark or gray soliton. Extracting the depleton effective mass reveals a super
heavy regime where the magnitude of the (negative) depleton mass exceeds the
mass of the finite Bose gas.
