  A detailed description is provided of a new Worm Algorithm, enabling the
accurate computation of thermodynamic properties of quantum many-body systems
in continuous space, at finite temperature. The algorithm is formulated within
the general Path Integral Monte Carlo (PIMC) scheme, but also allows one to
perform quantum simulations in the grand canonical ensemble, as well as to
compute off-diagonal imaginary-time correlation functions, such as the
Matsubara Green function, simultaneously with diagonal observables. Another
important innovation consists of the expansion of the attractive part of the
pairwise potential energy into elementary (diagrammatic) contributions, which
are then statistically sampled. This affords a complete microscopic account of
the long-range part of the potential energy, while keeping the computational
complexity of all updates independent of the size of the simulated system. The
computational scheme allows for efficient calculations of the superfluid
fraction and off-diagonal correlations in space-time, for system sizes which
are orders of magnitude larger than those accessible to conventional PIMC. We
present illustrative results for the superfluid transition in bulk liquid
helium-four in two and three dimensions, as well as the calculation of the
chemical potential of solid helium-four.
