Quantum phase transitions to charge-ordered and Wigner-crystal states under the interplay of lattice commensurability and long-range Coulomb interactions

The relationship among the Wigner crystal, charge ordering, and the Mott insulator is studied by the path-integral renormalization group method in two-dimensional systems with long-range Coulomb interaction. In contrast to the insensitivity of the Hartree-Fock results, the stability of the solid drastically decreases with the decrease in the lattice commensurability. The transition to liquid occurs at the electron gas parameter r(s) similar to 2 for the filling n = 1/2, showing a large reduction from r(s) similar to 35 in the continuum limit. A correct account of quantum fluctuations is crucial to understanding the charge-order stability generally observed only at simple fractional fillings and the nature of quantum liquids away from them.