The effect of correlation on the antiferromagnetic and paramagnetic phases of Hubbard's model of a half-filled narrow band are investigated using second-order perturbation theory. Employing the gap of the antiferromagnetic state as a variational parameter, it is shown that the increase of the bandwidth/potential-energy ratio leads to a phase transition into the paramagnetic state nearly where Mott has estimated it to occur. The convergence of the perturbation expansion is shown to be excellent at the transition.
The effect of correlation on the antiferromagnetic and paramagnetic phases of Hubbard's model of a half-filled narrow band are investigated using second-order perturbation theory. Employing the gap of the antiferromagnetic state as a variational parameter, it is shown that the increase of the bandwidth/potential-energy ratio leads to a phase transition into the paramagnetic state nearly where Mott has estimated it to occur. The convergence of the perturbation expansion is shown to be excellent at the transition.
Antiferromagnetic and metal to insulator transitions in the ground state of two-dimensional half-filled and nearly half-filled Hubbard models with the nearest neighbor and the second nearest neighbor transfers (- t and t ′ , respectively) are studied by using the Green's function approach with the self-energy up to the second order in the coupling constant U . For a choice of the parameter value t ′ / t =0.2 the half-filled model undergoes the first order phase transition between paramagnetic metallic (PM) phase and antiferromagnetic insulator (AFI) phase at U / t =4.0 while the first order transition between PM and antiferromagnetic metallic (AFM) phases takes place for nearly half-filled band. The one-electron spectral density is calculated for the PM, AFM, and AFI phases near the phase boundaries. In the PM phase the quasi-particle dispersion indicates the band narrowing from the Hartree-Fock results and the flat band behavior as was indicated by previous stadies and was observed in high- T c cuprates. The quasi-particle dispersion in the AFM phase is seen to be close to the Hartree-Fock results.
We have investigated the antiferromagnetic phase of two-dimensional (2D), three-dimensional (3D), and extended Hubbard models on a bipartite cubic lattice by means of the composite operator method within a two-pole approximation. This approach yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of both the model and the algebra. The complete phase diagram, as regards the antiferromagnetic and paramagnetic phases, has been drawn. We first reported, within a pole approximation, three kinds of transitions at half-filling: Mott-Hubbard, Mott-Heisenberg, and Heisenberg transitions. We have also found a metal-insulator transition, driven by doping, within the antiferromagnetic phase. This latter is restricted to a very small region near half-filling, and has, in contrast to what has been found by similar approaches, a finite critical Coulomb interaction as a lower bound at half-filling. Finally, it is worth noting that our antiferromagnetic gap has two independent components: one due to the antiferromagnetic correlations, and another coming from the Mott-Hubbard mechanism.
We study the transition from paramagnetic metal to paramagnetic insulator by finite temperature Quantum Monte-Carlo simulations for the 2D Hubbard model at half-filling. Working at the moderately high temperature T=0.33*t where the spin correlation length has dropped to 1.5 lattice spacings, and scanning the interaction strength U, we observe an unambiguous metal-insulator transition with onset at U_c=4t. In the metallic phase there are no indications of any `correlation narrowing' of the band width, nor for any decrease of spectral weight at the Fermi energy. The Mott-Hubbard gap opens gradually with increasing U and is accompanied by the formation of side bands near the Fermi energy. In the first stages of gap formation the gap opens at (pi,0), reminiscent of the `pseudogap' phenomenology in cuprate superconductors.
We study a two-band Hubbard model using the dynamical mean-field theory combined with the exact diagonalization method. At the electron density n=2, a transition from a band-insulator to a correlated semimetal occurs when the on-site Coulomb interaction U is varied for a fixed value of the charge-transfer energy Δ. At low temperature, the correlated semimetal shows ferromagnetism or superconductivity. With increasing doping ∣n−2∣, the ferromagnetic transition temperature rapidly decreases and finally becomes zero at a critical value of n. The second-order phase transition occurs at high temperature, while a phase separation of ferromagnetic and paramagnetic states takes place at low temperature. The superconducting transition temperature gradually decreases and finally becomes zero near n=1 (n=3) where the system is Mott insulator which shows antiferromagnetism at low temperature.
Antiferromagnetic and metal to insulator transitions in the ground state of a two dimensional half-filled Hubbard model with the nearest neighbor and the second nearest neighbor transfers (- t and t ′ , respectively) are studied by using the Hartree-Fock approximation. The results indicate that the phase diagram depends on the band structure or t ′ / t ratio; a discontinuous transition between the paramagnetic metallic (PM) and the antiferromagnetic insulator (AI) phases takes place for t ′ / t =0.2, while continuous transitions from PM to AM (antiferromagnetic metal) and then to AI phases take place for t ′ / t =0.5. The results are compared with those of the Gutzwiller approximation and discussed in the light of the other existing theories. The general importance of considering antiferromagnetism in this problem is emphasized.
We study by dynamical mean-field theory the ground state of a quarter-filled Hubbard model of two bands with different bandwidths. At half-filling, this model is known to display an orbital selective Mott transition, with the narrower band undergoing Mott localization while the wider one being still itinerant. At quarter-filling, the physical behavior is different and to some extent reversed. The interaction generates an effective crystal field splitting, absent in the Hamiltonian, that tends to empty the narrower band in favor of the wider one, which also become more correlated than the former at odds with the orbital selective paradigm. Upon increasing the interaction, the depletion of the narrower band can continue till it empties completely and the system undergoes a topological Lifshitz transition into a half-filled single-band metal that eventually turns insulating. Alternatively, when the two bandwidths are not too different, a first order Mott transition intervenes before the Lifshitz's one. The properties of the Mott insulator are significantly affected by the interplay between spin and orbital degrees of freedom.