Abstract We expose the relevance of double occupancy conservation symmetry in application of the Hubbard‐I approach to strongly correlated electron systems. We propose the utility of a composite method, viz. the Hubbard‐I method in conjunction with strong coupling perturbation expansion, for studying systems violating the afore‐mentioned symmetry. We support this novel approach by presenting a first successful Hubbard‐I type calculation for the description of the metal‐insulator paramagnetic Mott transition in a strongly correlated electron system with conserved double occupancies, which is a constrained Hubbard Hamiltonian equivalent to the Hubbard bond charge Hamiltonian at a symmetry point X = t. In particular, we obtain the phase diagram of this system for arbitrary fillings, as well as new, universal critical indices of the Mott transition at half‐filling in 1,2, and 3 dimensions. We also compare the Hubbard‐I band–splitting Mott transition description with results obtained using the standard Gutzwiller Approximation (GA), and show that the two approximate approaches lead to qualitatively different results. In contrast to the GA applied to the system studied here, the Hubbard‐I approach compares favorably with known exact results for the d = 1 dimensional chain.
The problem of deconfinement phases in strongly correlated systems is discussed. In space–time dimension
d=3+1 , a competition of confinement and Coulomb phases occurs, but in
d=2+1 the confining phase dominates owing to monopole proliferation, but Dirac points can change the situation. Combining the Kotliar–Ruckenstein representation and fractionalized spin-liquid deconfinement picture, the Mott transition and Hubbard subbands are treated, general expressions in the case of an arbitrary bare band spectrum being obtained. The transition into a metallic state is determined by condensation of a gapless boson mode. The spectrum picture in the insulating state is considerably influenced by the spinon spin-liquid spectrum and hidden Fermi surface.
We argue that the binding between doubly occupied (doublon) and empty (holon) sites governs incoherent excitations and plays a key role in the Mott transition in strongly correlated Mott-Hubbard systems. We construct a new saddle-point solution with doublon-holon binding in the Kotliar-Ruckenstein slave-boson functional integral formulation of the Hubbard model. On a half-filled honeycomb lattice and square lattice, the ground state is found to exhibit a continuous transition from a paramagnetic semimetal/metal to an antiferromagnetic-ordered Slater insulator with coherent quasiparticles at
Uc1, followed by a Mott transition into an electron-fractionalized AF
∗ phase without coherent excitations at
Uc2. Such a phase structure appears to be generic for bipartite lattices without frustration. We show that doublon-holon binding unites the three important ideas of strong correlation: coherent quasiparticles, incoherent Hubbard bands, and deconfined Mott insulator.