A new numerical algorithm for interacting fermion systems to treat the grand-canonical ensemble is proposed and examined by extending the path-integral renormalization group method. To treat the grandcanonical ensemble, the particle-hole transformation is applied to the Hamiltonian and basis states. In the interaction-term projection, the Stratonovich-Hubbard transformation which hybridizes up and down spin electrons is introduced. By using this method, the phase diagram of the two-dimensional Hubbard model with next-nearest-neighbor transfer is accurately determined by treating the filling-control (FC) and bandwidth-control (BC) Mott transitions on the same ground. A V-shaped Mott insulating phase is obtained in the plane of the chemical potential and the Coulomb interaction, where the transitions at the corner (BC) and the edges (FC) show contrasted characters with large critical fluctuations near the edges coexisting with the first-order transition at the corner. This contrasted behavior is shown to be consistent with the V-shape structure of the phase boundary because of a general relation, in which the slope of the metal-insulator transition line in the phase diagram is expressed by thermodynamic quantities. The V-shaped opening of the Mott gap is favorably compared with the experimental results of the transition metal oxides.
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