Figure 1
Actual configurations for N = 6 (upper) and N = 29 (lower) electrons of the Harmonic trap (left) and Laughlin ν = 1 state (right). The panels show the maximal weight configurations (rightmost), maximal weight configurations actually obtained in the MC simulation of the system (second from right) and three randomly chosen configurations (left). These are marked in the histogram of the corresponding probability density distribution. ρ0 is the geometric average of the probability densities of the generated MC samples. In all panels 104 independent configurations where generated. For comparison, we also plot the function \(\rho {\rm{l}}{\rm{n}}\,{(1/\rho )}^{\frac{d}{2}-1}\), where ρ is the probability density (see main text for a justification). Note how randomly chosen configurations show very little signs of forming a crystal. Even the state with the highest observed probability density, among the 104 MC samples, is quite far from the maximal weight configuration.
