The Worm Algorithm is a versatile Path Integral Monte Carlo method which circumvents some of the near-critical limitations present in local update algorithms, such as Metropolis. It achieves this by sampling an extended configuration space called the Z-Sector, which contains the unphysical open worldlines corresponding to off-diagonal elements in the density matrix. 

In this work, the worm algorithm is applied to the Bose-Hubbard model: a prototypical model for interacting bosons, and which can be experimentally realized by optical lattices. The B-H model experiments a quantum phase transition which is of the Berezinskii–Kosterlitz–Thouless type in 1D. By simulating equilibrium configurations using the worm algorithm and measuring the superfluid index, the well known phase diagram of the B-H model is captured.