Surface worm algorithm for abelian Gauge-Higgs systems on the lattice

Abstract The Prokof’ev–Svistunov worm algorithm was originally developed for models with nearest neighbor interactions that in a high temperature expansion are mapped to systems of closed loops. In this work we present the surface worm algorithm (SWA) which is a generalization of the worm algorithm concept to abelian Gauge–Higgs models on a lattice which can be mapped to systems of surfaces and loops (dual representation). Using Gauge–Higgs models with gauge groups Z 3 and U(1) we compare the SWA to the conventional approach and to a local update in the dual representation. For the Z 3 case we also consider finite chemical potential where the conventional representation has a sign problem which is overcome in the dual representation. For a wide range of parameters we find that the SWA clearly outperforms the local update.