Near self-duality and spatial reorganization of anyon vortex lattices

Abstract

Contact attraction drives the self-generated vortex lattice of a trapped anyon gas towards self-duality, but integrated energies do not reveal where the remaining departure from it is located. We address this question in the almost-bosonic Chern--Simons--Schrödinger average-field model using a positive, gauge-invariant local defect that measures the covariant kinetic energy in excess of the magnetic bound. Numerically computed low-energy states at three statistical fluxes show that, as the stability line is approached, the integrated defect falls by about two orders of magnitude while the density modulation grows, so that magnetic saturation and density uniformity separate. The residual defect concentrates in a vortex-free outer shell that carries unscreened statistical flux. There it reduces to a smooth radial mismatch between the statistical flow and the density decay, which the interior lattice cannot cancel, whereas the covariant kinetic and amplitude-gradient energies show no comparable enrichment. The effect is robust to grid and box refinement, while its magnitude depends on flux and on the low-energy branch. Exact dilation and contact-response identities relate the squared energy to the density shape and provide consistency checks. Repulsion produces the opposite trend: a smoother density with a larger defect.