Generalization of vortex-lattice melting results to anisotropic traps and finite-size effects

Determine how the established vortex-lattice melting transition and associated critical behavior in rapidly rotating Bose gases—known from isotropic, toroidal-geometry studies that find a transition from a Gross-Pitaevskii vortex lattice to a Laughlin-like fractional quantum Hall ground state around filling factor ν≈6—generalize to anisotropic trapping potentials, and quantify how finite-size constraints on the vortex lattice shift or modify the transition point in the lowest-Landau-level-projected cylindrical geometry.

Background

Earlier exact diagonalization and Bogoliubov analyses in isotropic or torus geometries have established a quantum phase transition around ν≈6 from a vortex lattice described by Gross-Pitaevskii theory to a Laughlin-like fractional quantum Hall phase. The present work considers an anisotropic trap under rapid rotation, mapping the system to a Landau-gauge cylinder with edges, and explores phases via LLL projection, ED, and DMRG.

The authors highlight that anisotropy and finite-size constraints (including edge effects) can qualitatively alter the phase behavior. They explicitly state that the generalization of these landmark results to anisotropic traps and the impact of finite-size constraints on the transition point are not yet clarified in the literature, motivating a targeted investigation in this geometry.