Quantum Melting on a Lattice and a Delocalization Transition

We have performed a numerical study of the structural and IM phase transitions in 2D fermionic systems with Hamiltonian Eq. (1). We argue that the structural transition on a lattice is not of the first order in all cases considered. We think that the origin of the transition is an avoided crossing of the ground state and the defect states in the Wigner crystal with the same total quasimomentum. This simple picture implies that the critical value of J is determined by the defect with the lowest energy Δ at J=0. To illustrate our point the data for 1D systems with Coulomb interaction and with next-nearest neighbor interactions are also presented. The possibility of the delocalized phase above the transition to be superconducting is discussed.