Vortex patterns in the almost-bosonic anyon gas

Abstract

We study theoretically and numerically the ground state of a gas of 2D abelian anyons in an external trapping potential. We treat anyon statistics in the magnetic gauge picture, perturbatively around the bosonic end. This leads to a mean-field energy functional, whose ground state displays vortex lattices similar to those found in rotating Bose-Einstein condensates. A crucial difference is however that the vortex density is proportional to the underlying matter density of the gas.

Figures (6)

• Figure 1: Mean-field approximation $|u ^{\rm af}_\beta| ^2$ for the density of an anyon gas with total magnetic flux $\beta$ in a quadratic trap $V(\mathbf{x}) = |\mathbf{x}| ^2$, at $\beta= 5,15,25,140$.
• Figure 2: Mean-field approximation $|u ^{\rm af}_\beta| ^2$ for the density of an anyon gas with total magnetic flux $\beta$ in a quartic trap $V(\mathbf{x}) = |\mathbf{x}| ^4$, at $\beta= 55,90,140,195$.
• Figure 3: Determination of the thermodynamic energy $e(1,1)$ of the homogeneous mean-field anyon gas at density $\rho = 1$ and total magnetic flux $\beta = 1$. Extrapolated from numerical data with quadratic (above) and quartic (below) traps.
• Figure 4: Theoretical (red) and numerical (blue) rotationally-averaged density profiles for the mean-field anyon gas. Top panel: quadratic trap $V(\mathbf{x}) = |\mathbf{x}|^2,$ magnetic flux $\beta = 90$. Bottom panel: quartic trap $V(\mathbf{x}) = |\mathbf{x}|^4$, magnetic flux $\beta = 140$.
• Figure 5: Theoretical (red) versus numerical (blue) vortex densities in the mean-field anyon gas. Top panel: quadratic $V(\mathbf{x}) = |\mathbf{x}|^2$, magnetic flux $\beta = 140$. Bottom panel: quartic trap $V(\mathbf{x}) = |\mathbf{x}|^4$, magnetic flux $\beta = 195$.