  Understanding the stability of strongly correlated phases of matter when
coupled to environmental degrees of freedom is crucial for identifying the
conditions under which these states may be observed. Here, we focus on the
paradigmatic one-dimensional Bose-Hubbard model, and study the stability of the
Luttinger liquid and Mott insulating phases in the presence of local particle
exchange with site-independent baths of non-interacting bosons. We perform a
numerically exact analysis of this model by adapting the recently developed
wormhole quantum Monte Carlo method for retarded interactions to a
continuous-time formulation with worm updates; we show how the wormhole updates
can be easily implemented in this scheme. For an Ohmic bath, our numerical
findings confirm the scaling prediction that the Luttinger-liquid phase becomes
unstable at infinitesimal bath coupling. We show that the ensuing phase is a
long-range ordered superfluid with spontaneously-broken U(1) symmetry. While
the Mott insulator remains a distinct phase for small bath coupling, it
exhibits diverging compressibility and non-integer local boson occupation in
the thermodynamic limit. Upon increasing the bath coupling, this phase
undergoes a transition to a long-range ordered superfluid. Finally, we discuss
the effects of super-Ohmic dissipation on the Luttinger-liquid phase. Our
results are compatible with a stable dissipative Luttinger-liquid phase that
transitions to a long-range ordered superfluid at a finite system-bath
coupling.
