Quantum Phase Transitions to Charge Order and Wigner Crystal Under Interplay of Lattice Commensurability and Long-Range Coulomb Interaction

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Relationship among Wigner crystal, charge order and Mott insulator is studied by the path-integral renormalization group method for two-dimensional lattices with long-range Coulomb interaction. In contrast to Hartree-Fock results, the solid stability drastically increases with lattice commensurability. The transition to liquid occurs at the electron gas parameter rₛ 2 for the filling n=1/2 showing large reduction from rₛ 35 in the continuum limit. Correct account of quantum fluctuations are crucial to understand charge-order stability generally observed only at simple fractional fillings and nature of quantum liquids away from them.