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.
The ground-state phase diagram of the half-filled two-leg Hubbard ladder with intersite Coulomb repulsions and exchange coupling is studied by using the strong-coupling perturbation theory and the weak-coupling bosonization method. Considered here as possible ground states of the ladder model are four types of density-wave states with different angular momentum
(s-density-wave state, p-density-wave state, d-density-wave state, and f-density-wave state) and four types of quantum disordered states, i.e., Mott insulating states
(S-Mott, D-Mott, ${S}^{\ensuremath{'}}$-Mott, and ${D}^{\ensuremath{'}}$-Mott states, where S and D stand for s- and d-wave symmetry). The s-density-wave state, the d-density-wave state, and the D-Mott state are also known as the charge-density-wave state, the staggered-flux state, and the rung-singlet state, respectively. Strong-coupling approach naturally leads to the Ising model in a transverse field as an effective theory for the quantum phase transitions between the staggered-flux state and the D-Mott state and between the charge-density-wave state and the S-Mott state, where the Ising ordered states correspond to doubly degenerate ground states in the staggered-flux or the charge-density-wave state. From the weak-coupling bosonization approach it is shown that there are three cases in the quantum phase transitions between a density-wave state and a Mott state: the Ising
(Z2) criticality, the
SU(2)2 criticality, and a first-order transition. The quantum phase transitions between Mott states and between density-wave states are found to be the U(1) Gaussian criticality. The ground-state phase diagram is determined by integrating perturbative renormalization-group equations. It is shown that the S-Mott state and the staggered-flux state exist in the region sandwiched by the charge-density-wave phase and the D-Mott phase. The p-density-wave state, the ${S}^{\ensuremath{'}}$-Mott state, and the ${D}^{\ensuremath{'}}$-Mott state also appear in the phase diagram when the next-nearest-neighbor repulsion is included. The correspondence between Mott states in extended Hubbard ladders and spin-liquid states in spin ladders is also discussed.
We investigate the ground-state phase diagram of the quantum mixed spin chain in which two
S=21 and two S =1 spins are arranged alternatively and isotropic exchange interactions between nearest-neighboring pairs of spins are assumed. Guided by our previous results [J. Phys. Soc. Jpn. 67 (1998) 1000] for a few limiting cases of the exchange interactions, we carry out a density-matrix renormalization-group calculation to determine the ground-state phase diagram in detail. From the gapless points of the singlet-triplet energy gap, five boundary lines are determined, which divide the phase diagram into six regions. In three regions the ground states with the Haldane-phase character appear, while in the remaining three regions those with the dimer character appear. We also present a characterization of the phases concerning how the ground state in each phase is represented in the framework of the valence-bond-solid (VBS) picture. Making use of the matrix-product wave function, we classify the VBS pictures and interpret the ground-state phase diagram in terms of symmetries schematically related to the VBS pictures. We investigate the ground-state nearest-neighboring two-spin correlation functions and a kind of string order parameters, by which we confirm the validity of the characterization.
Charge and spin orderings are studied on the simplest one-dimensional (1D) and the two-dimensional (2D) square lattices within the generalized Falicov-Kimball model with Hund coupling between localized and itinerant electrons. Using the restricted phase diagram method (RPDM), a number of simple rules of formation of various sorts of ground-state phases have been detected. In particular, relationships between density of current carriers (electrons or holes) and type of charge and magnetic arrangement have been determined. In two dimensions in the mixed-valence regime, only axial stripes (vertical or horizontal) have been found for intermediate values of the coupling constants. They are composed of ferromagnetic or antiferromagnetic chains interchanged with nonmagnetic ones. For band fillings close to the half filling, stripe phases oriented along one of the main diagonal direction are formed. The results suggest the possibility of tuning modulations of charge and magnetic superstructures with a change in doping.
The cluster slave-spin method is employed to investigate systematically the ground state properties of the Hubbard model on a square lattice with doping $\ensuremath{\delta}$ and coupling strength
U being its parameters. At half-filling, a relation between the staggered magnetization
M and the antiferromagnetic (AFM) gap ${\mathrm{\ensuremath{\Delta}}}_{\text{AFM}}$ is established in the small
U limit to compare with that from the Hartree-Fock theory, and a first-order metal-insulator Mott transition in the paramagnetic state is substantiated, which is characterized by discontinuities and hystereses at
UMott=10t. The interaction
Uc for the crossover in the AFM state, separating the weak- and strong-coupling regimes, is found to remain almost unchanged with large dopings, and smaller than
UMott at half-filling because of long range AFM correlations. Finally, an overall phase diagram in the $U\ensuremath{-}\ensuremath{\delta}$ plane is presented, which is composed of four regimes: the AFM insulator at half-filling, the AFM metal with the compressibility $\ensuremath{\kappa}>0$ or $\ensuremath{\kappa}<0$, and the paramagnetic metal, as well as three phase transitions: (i) From the AFM metal to the paramagnetic metal, (ii) between the AFM metal phases with positive and negative $\ensuremath{\kappa}$, and (iii) separating the AFM insulating phase at $\ensuremath{\delta}=0$ from the AFM metal phase for $\ensuremath{\delta}>0$.