The Hydra algorithm for simulating coupled U(1) systems

Modified quantum Bose-Hubbard models and their classical counterparts, coupled XY models, have recently been shown to exhibit interesting phase diagrams, where the confinement/deconfinement of fractional vortices can lead to disordered phases with global U(1) symmetry that overall retain the discrete relative order. Whereas numerical studies in (1+1)D can be done efficiently via tensor network and DMRG studies, they become much more challenging in dimensions (2+1)D and higher. Here, we harness the efficiency of the worm algorithm at simulating XY models through nonlocal updates in their dual space. Adapting the worm algorithm to classical coupled XY models proves non-trivial and requires the interplay of many types of worms that can span the system whilst maintaining a modified Gauss' law constraint at each site. In this presentation, I show a modified worm algorithm where the head of the worms can fractionalize into many heads before eventually recombining. I will comment on the implication of such splinter and recombination events of the many-headed-worm, called a hydra, for the observation and measurement of confinement-deconfinement transitions in coupled XY models. Finally, I will provide a roadmap to where such coupled XY models and their quantum analogues, such as modified Bose-Hubbard models, can occur.