Worm Algorithm

Worm Algorithm (Prokof'ev & Svistunov 1998): In the worldline QMC representation, particles trace paths through imaginary time τ∈[0,β]. The worm algorithm samples these configurations by introducing an open string (the "worm") with head (Ira) and tail (Masha) that performs local moves — extending, retracting, and jumping — until it closes into a loop, proposing a new closed worldline configuration. This gives ergodic sampling of the grand-canonical ensemble. The worm head/tail are shown in yellow/orange; closed worldlines appear as colored loops. The algorithm is exact (no sign problem for bosons) and efficient even near phase transitions.