We use the cluster-variation method to examine the phase diagram of the spin-1/2 XXZ model. The clusters used consist of two neighboring spins. With this method, we calculate global phase diagrams for arbitrary values of the anisotropy ${\mathit{J}}_{\mathit{z}}$ /J and for arbitrary external magnetic fields. Lattices with different values of the coordination number z are considered. Analytic expressions are found for nearly all phase boundaries; the remaining phase boundary is located numerically. Despite some problems at low temperature, the results based on this approach are in quite good agreement with the results from series-expansion methods. A connection is made with the Hubbard model, which can be mapped onto the XXZ Hamiltonian in the limit of strong on-site attraction.We use the cluster-variation method to examine the phase diagram of the spin-1/2 XXZ model. The clusters used consist of two neighboring spins. With this method, we calculate global phase diagrams for arbitrary values of the anisotropy ${\mathit{J}}_{\mathit{z}}$/J and for arbitrary external magnetic fields. Lattices with different values of the coordination number z are considered. Analytic expressions are found for nearly all phase boundaries; the remaining phase boundary is located numerically. Despite some problems at low temperature, the results based on this approach are in quite good agreement with the results from series-expansion methods. A connection is made with the Hubbard model, which can be mapped onto the XXZ Hamiltonian in the limit of strong on-site attraction.

Physical review. B, Condensed matterJun 1, 199125 citations

Exact magnetic phase diagram of the one-dimensional Hubbard model

Chia‐Wei Yang, ARMEN N. KOCHARIAN, Y. L. Chiang

Physica B Condensed MatterJun 1, 20000 citations

Excitonic insulator state in the two-orbital Hubbard model: Variational cluster approach

Tatsuya Kaneko, Kazuhiro Seki, Y. Ohta

The variational cluster approximation is used to study the spontaneous symmetry breaking of the excitonic insulator (EI) state in the two-orbital Hubbard model defined on the two-dimensional square lattice. Evaluating the order parameter of the EI state, staggered magnetization, and number of particles on each orbital, we obtain the ground-state phase diagram of the model in a wide parameter space of the intra and interorbital Coulomb interactions. We also calculate the single-particle and anomalous Green's functions. We show that the normal metallic phase is unstable to the formation of the EI state and the EI phase appears in a wide parameter region between the band-insulator and Mott-insulator phases.The variational cluster approximation is used to study the spontaneous symmetry breaking of the excitonic insulator (EI) state in the two-orbital Hubbard model defined on the two-dimensional square lattice. Evaluating the order parameter of the EI state, staggered magnetization, and number of particles on each orbital, we obtain the ground-state phase diagram of the model in a wide parameter space of the intra and interorbital Coulomb interactions. We also calculate the single-particle and anomalous Green's functions. We show that the normal metallic phase is unstable to the formation of the EI state and the EI phase appears in a wide parameter region between the band-insulator and Mott-insulator phases.

Physical Review BApr 23, 201268 citations

Magnetic and thermodynamical properties of the simple-cubic Hubbard model

Y. Kakehashi, Hideo Hasegawa

Magnetic and thermodynamical properties of the half-filled Hubbard model on the simple-cubic lattice have been investigated by using the two analytical theories for band magnetism: the single-site spin fluctuation (SSF) theory proposed independently by Hubbard and Hasegawa and the Gutzwiller-type variational approach (VA) developed by Kakehashi and Fulde. We have calculated, as a function of the temperature T and the electron-electron interaction U, the sublattice magnetization, amplitude of local moments, susceptibilities, energy, and entropy, from which the U-T phase diagram is obtained. Our ground-state results, particularly of the VA, are in good agreement with those obtained in the variational Monte Carlo calculations performed by Yokoyama and Shiba. Our finite-temperature calculations are compared with those in the recent Monte Carlo (MC) simulations made by Hirsch. It is shown that, as far as local quantities such as the amplitude of local moments and the Curie constants are concerned, our results are consistent with the MC results. It is realized, however, that the antiferromagnetic correlation is much overestimated in a small 4\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}4 cluster in Hirsch's MC simulation, yielding N\'eel temperatures, ${T}_{N}$ , about 70% higher than those in the mean-field-type theories of the SSF and VA approaches.Magnetic and thermodynamical properties of the half-filled Hubbard model on the simple-cubic lattice have been investigated by using the two analytical theories for band magnetism: the single-site spin fluctuation (SSF) theory proposed independently by Hubbard and Hasegawa and the Gutzwiller-type variational approach (VA) developed by Kakehashi and Fulde. We have calculated, as a function of the temperature T and the electron-electron interaction U, the sublattice magnetization, amplitude of local moments, susceptibilities, energy, and entropy, from which the U-T phase diagram is obtained. Our ground-state results, particularly of the VA, are in good agreement with those obtained in the variational Monte Carlo calculations performed by Yokoyama and Shiba. Our finite-temperature calculations are compared with those in the recent Monte Carlo (MC) simulations made by Hirsch. It is shown that, as far as local quantities such as the amplitude of local moments and the Curie constants are concerned, our results are consistent with the MC results. It is realized, however, that the antiferromagnetic correlation is much overestimated in a small 4\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}4 cluster in Hirsch's MC simulation, yielding N\'eel temperatures, ${T}_{N}$, about 70% higher than those in the mean-field-type theories of the SSF and VA approaches.

Physical review. B, Condensed matterMay 1, 198831 citations

On the Phase Diagram of the Hubbard Model

J. Monecke

physica status solidi (b)Mar 1, 19767 citations

{\mathit{J}}_{\mathit{z}}

/J and for arbitrary external magnetic fields. Lattices with different values of the coordination number z are considered. Analytic expressions are found for nearly all phase boundaries; the remaining phase boundary is located numerically. Despite some problems at low temperature, the results based on this approach are in quite good agreement with the results from series-expansion methods. A connection is made with the Hubbard model, which can be mapped onto the XXZ Hamiltonian in the limit of strong on-site attraction.

{T}_{N}

, about 70% higher than those in the mean-field-type theories of the SSF and VA approaches.