Crystal mean field based trial wavefunctions for the FQHE ground states

Employing the Haldane-Rezayi periodic representation, the crystalline determinantal Hall crystal mean field solutions derived in previous works are used to construct variational wavefunctions for the FQHE at $\nu=1/q$. The proposed states optimize the short range correlations in a similar measure as the Laughlin ones, since the zero of the states when the coordinates of two particles join is of order $q$. However, the proposed wavefunctions also incorporate the crystalline correlations of the mean field problem, through a determinantal mean field function entering their construction. The above properties, lead to the expectation that the considered states can be competitive in energy per particle with the Laughlin ones. Their similar structure also could explain way the breaking of the translation invariance in the FQHE ground states can result to be a weak one, which after disregarded, produce the Laughlin states as good approximations. Calculation for checking these possibilities are under consideration.