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Relationship among Wigner crystal, charge order and Mott insulator is studiedby the path-integral renormalization group method for two-dimensional latticeswith long-range Coulomb interaction. In contrast to Hartree-Fock results, thesolid stability drastically increases with lattice commensurability. Thetransition to liquid occurs at the electron gas parameter $r_s \sim 2$ for thefilling $n=1/2$ showing large reduction from $r_s \sim 35$ in the continuumlimit. Correct account of quantum fluctuations are crucial to understandcharge-order stability generally observed only at simple fractional fillingsand nature of quantum liquids away from them.Comment: 4 pages including 7 figure

physical review letters

Quantum Phase Transitions to Charge-Ordered and Wigner-Crystal States under the Interplay of Lattice Commensurability and Long-Range Coulomb Interactions