Interplay between condensation, vortex lattices, and strongly correlated phases

Characterize the interplay among Bose–Einstein condensation, vortex lattice formation, and strongly correlated fractional quantum Hall phases in a rapidly rotating anisotropic Bose gas on a cylindrical Landau-gauge geometry, including identifying phase boundaries and the mechanisms governing transitions between these regimes.

Background

The paper unifies weakly interacting condensates, multiple vortex lattice structures, and strongly correlated Laughlin-like phases within a single LLL-projected model controlled by interaction strength and anisotropy. Despite progress, a comprehensive understanding of how these regimes interact and transition into one another in the anisotropic cylindrical geometry remains incomplete.

The authors explicitly state that this interplay is still an open and intriguing problem, underscoring the need for a systematic theoretical treatment that bridges symmetry-broken superfluid phases and topologically ordered quantum Hall phases in finite, edge-influenced samples.