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A new numerical algorithm for interacting fermion systems to treat thegrand-canonical ensemble is proposed and examined by extending thepath-integral renormalization group method. To treat the grand-canonicalensemble, the particle-hole transformation is applied to the Hamiltonian andbasis states. In the interaction-term projection, the Stratonovich-Hubbardtransformation which hybridizes up and down spin electrons is introduced. Byusing this method, the phase diagram of the two-dimensional Hubbard model withnext-nearest-neighbor transfer is accurately determined by treating thefilling-control (FC) and bandwidth-control (BC) Mott transitions on the sameground. A V-shaped Mott insulating phase is obtained in the plane of thechemical potential and the Coulomb interaction, where the transitions at thecorner (BC) and the edges (FC) show contrasted characters with large criticalfluctuations near the edges coexisting with the first-order transition at thecorner. This contrasted behavior is shown to be consistent with the V-shapestructure of the phase boundary because of a general relation, in which theslope of the metal-insulator transition line in the phase diagram is expressedby thermodynamic quantities. The V-shaped opening of the Mott gap is favorablycompared with the experimental results of the transition metal oxides.Comment: 17 pages, 14 figure

journal of the physical society of japan

Precise Determination of Phase Diagram for Two-Dimensional Hubbard Model with Filling- and Bandwidth-Control Mott Transitions: Grand-Canonical Path-Integral Renormalization Group Approach