Possible fractional quantum Hall effect and Wigner crystal states in two-dimensional Coulomb gases as a result of anyon correlations

Recently, we have derived an approximate analytic formula for the ground state energy of (2D) charged anyon gas. This result allows us in the present paper to estimate the exchangecorrelation energy, which is as it is well known from a literature the difference of the ground state energy and the Hartree-Fock energy, for fermions with the anyon parameter ν=1, and to formulate the anyon correlation energy for other ν<1. The minima of the last one for all fixed values of ν as well as the minima of the ground state energy at the same ν are only the ν dependent, which means they are only the anyon statistics dependent with no effect of the Coulomb interaction. From this, we conclude that there should appear the localized real space macroscopic structure for any fixed ν from ν<1. For instance, since the Landau level fillingfactor (LLFF) of the fractional quantum Hall effect (FQHE) quasi-particles is equal to the anyon parameter then these quasi-particles should condense in the some real space structure at this LLFF, forming the FQHE plateau and showing that the FQHE is a result of anyoncorrelations. On the other hand, expressing the above mentioned minima function of ν through the density parameter rs of the Coulomb gas, we obtain the values of rs, for which the 2D Wigner crystal (WC) can be observed. It is interesting that the simultaneous observation of the FQHE and WC states in accord with our consideration.

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