Vortex patterns of a 2D rotating Bose-Einstein condensate at the critical rotational speed

We introduce a GPU-accelerated variational framework with exact projection onto the Lowest Landau Level to probe vortex patterns in rapidly rotating two-dimensional Bose-Einstein condensates. For repulsive interactions, our approach faithfully reproduces Abrikosov vortex lattices, achieving quantitative alignment with Thomas-Fermi theory and the Abrikosov constant, while underscoring the profound analogy between superfluid vortex ordering and Abrikosov lattices in type-II superconductors. In the attractive regime, we reveal that weak attractions sustain stable vortex arrays, whereas stronger attractions quench vortices, trigger radial contraction, and culminate in collapse at the Gagliardo-Nirenberg threshold. These findings deliver a cohesive numerical benchmark for vortex formation and collapse dynamics, forging a rigorous link between superfluidity and superconductivity in rotating quantum matter.