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Filling-control metal-insulator transition on the two-dimensional Hubbardmodel is investigated by using the correlator projection method, which takesinto account momentum dependence of the free energy beyond the dynamicalmean-field theory. The phase diagram of metals and Mott insulators is analyzed.Lifshitz transitions occur simultaneously with metal-insulator transitions atlarge Coulomb repulsion. On the other hand, they are separated each other forlower Coulomb repulsion, where the phase sandwiched by the Lifshitz andmetal-insulator transitions appears to show violation of the Luttinger sumrule. Through the metal-insulator transition, quasiparticles retain nonzerorenormalization factor and finite quasi-particle weight in the both sides ofthe transition. This supports that the metal-insulator transition is caused notby the vanishing renormalization factor but by the relative shift of the Fermilevel into the Mott gap away from the quasiparticle band, in sharp contrastwith the original dynamical mean-field theory. Charge compressibility divergesat the critical end point of the first-order Lifshitz transition at finitetemperatures. The origin of the divergence is ascribed to singular momentumdependence of the quasiparticle dispersion.Comment: 24 pages including 10 figure

Fate of Quasiparticle at Mott Transition and Interplay with Lifshitz Transition Studied by Correlator Projection Method