  A ground state path integral quantum Monte Carlo algorithm is introduced that
allows for the study of entanglement in lattice bosons at zero temperature. The
R\'enyi entanglement entropy between spatial subregions is explored across the
phase diagram of the one dimensional Bose-Hubbard model for systems consisting
of up to $L=256$ sites at unit-filling without any restrictions on site
occupancy, far beyond the reach of exact diagonalization. The favorable scaling
of the algorithm is demonstrated through a further measurement of the R\'enyi
entanglement entropy at the two dimensional superfluid-insulator critical point
for large system sizes, confirming the existence of the expected entanglement
boundary law in the ground state. The R\'enyi estimator is extended to measure
the symmetry resolved entanglement that is operationally accessible as a
resource for experimentally relevant lattice gases with fixed total particle
number.
