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Physical review. B, Condensed matter

Ferromagnetism in an orbitally degenerate Hubbard model

J. Kuei, Richard T. Scalettar

Published Jun 1, 1997• 30 citations
Publisher

Abstract

We study the magnetic phase diagram of a one-dimensional, orbitally degenerate Hubbard model using the Lanczos algorithm to project out the ground state. Using lattices larger than those previously explored with diagonalization approaches, we find a phase diagram which is in much better agreement with a strong coupling analysis. In addition to determining the phase diagram by calculating the spin sector of minimum energy, we also show results for the spin-spin correlations and participation ratio, which further characterize the magnetic order and the itineracy of the electrons. We then describe results for the case when the intersite hybridization is different for the two orbitals.

DOI
10.1103/physrevb.55.14968

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We study the magnetic phase diagram of a one-dimensional, orbitally degenerate Hubbard model using the Lanczos algorithm to project out the ground state. Using lattices larger than those previously explored with diagonalization approaches, we find a phase diagram which is in much better agreement with a strong coupling analysis. In addition to determining the phase diagram by calculating the spin sector of minimum energy, we also show results for the spin-spin correlations and participation ratio, which further characterize the magnetic order and the itineracy of the electrons. We then describe results for the case when the intersite hybridization is different for the two orbitals.
We studied ferromagnetism in the one-dimensional Hubbard model with doubly degenerate atomic orbitals by means of the density-matrix renormalization-group method and obtained the ground-state phase diagrams. It was found that ferromagnetism is stable from low to high (0<n<1.75)(0<n<1.75)(0<n<1.75) electron density when the interactions are sufficiently strong. The quasi-long-range order of triplet superconductivity coexists with the ferromagnetic order for a strong Hund coupling region, where the interorbital interaction ${U}^{\ensuremath{'}}\ensuremath{-}J$ is attractive. At quarter-filling (n=1),(n=1),(n=1), the insulating ferromagnetic state appears, accompanying orbital quasi-long-range order. For low densities (n<1),(n<1),(n<1), ferromagnetism occurs owing to the ferromagnetic exchange interaction caused by virtual hoppings of electrons, the same as in the quarter-filled system. This comes from separation of the charge and spin-orbital degrees of freedom in the strong-coupling limit. This ferromagnetism is fragile against variation of band structure. For high densities (n>1),(n>1),(n>1), the phase diagram of the ferromagnetic phase is similar to that obtained in infinite dimensions. In this case, the double exchange mechanism is operative for stabilizing the ferromagnetic order and this long-range order is robust against variation of the band dispersion. A partially polarized state appears in the density region $1.68\ensuremath{\lesssim}n\ensuremath{\lesssim}1.75$ and phase separation occurs for n just below the half-filling (n=2).(n=2).(n=2).
Correlations of a one-dimensional doubly degenerate Hubbard model are studied for the one-quarter-filled case. Exact calculations on a four-site lattice show that a ferromagnetic state exists in the strong-coupling regime. For a one-dimensional chain, a strong-coupling effective Hamiltonian was studied using a self-consistent calculation, a high-temperature expansion, and quantum Monte Carlo simulations. The results provide information on the parameters needed for ferromagnetic correlations, and the temperature dependence of the spin and orbital correlations.
We present the zero-temperature phase diagram of the one-dimensional t2g{t}_{2\mathrm{g}}t2g​-orbital Hubbard model, obtained using the density-matrix renormalization group and Lanczos techniques. Emphasis is given to the case of the electron density n=5n=5n=5 corresponding to five electrons per site, while several other cases for electron densities between n=3n=3n=3 and 6 are also studied. At n=5n=5n=5, our results indicate a first-order transition between a paramagnetic (PM) insulator phase, with power-law slowly decaying correlations, and a fully polarized ferromagnetic (FM) state by tuning the Hund's coupling. The results also suggest a transition from the n=5n=5n=5 PM insulator phase to a metallic regime by changing the electron density, either via hole or electron doping. The behavior of the spin, charge, and orbital correlation functions in the FM and PM states are also described in the text and discussed. The robustness of these two states against varying parameters suggests that they may be of relevance in quasi-one-dimensional Co-oxide materials, or even in higher dimensional cobaltite systems as well.
We exactly diagonalize the effective Hamiltonian obtained from the Hubbard model in the strong-coupling limit for a two-dimensional $\sqrt{10}\ifmmode\times\else\texttimes\fi{}\sqrt{10}$ size square lattice. The effective Hamiltonian operates on a restricted Hilbert space containing only states with singly occupied sites, which makes the diagonalization possible within reasonable computational time for the above lattice. The ground-state energy and wave function are obtained for several values of the coupling ratio tU\frac{t}{U}Ut​ and the doping fraction xxx. We find three different phases in the (x,tUx,\frac{t}{U}x,Ut​) phase diagram. The first is characterized by antiferromagnetic order which extends to the longest possible distance in the 10-site system. The second and third phases are characterized by antiferromagnetic and ferromagnetic short-range correlations, respectively. We comment on the possible relevance of the results to the recently discovered high-temperature copper-oxide superconductors.
We study the phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping using exact diagonalization, the density-matrix renormalization group, the Edwards variational ansatz, and an adaptation of weak-coupling calculations on the two-chain Hubbard model. We find that a substantial region of the strong-coupling phase diagram is ferromagnetic, and that three physically different limiting cases are connected in one ferromagnetic phase. At a point in the phase diagram at which there are two Fermi points at weak coupling, we study carefully the phase transition from the paramagnetic state to the fully polarized one as a function of the on-site Coulomb repulsion. We present evidence that the transition is second order and determine the critical exponents numerically. In this parameter regime, the system can be described as a Luttinger liquid at weak coupling. We extract the Luttinger-liquid parameters and show how their behavior differs from that of the nearest-neighbor Hubbard model. The general weak-coupling phase diagram can be mapped onto that of the two-chain Hubbard model. We exhibit explicitly the adapted phase diagram and determine its validity by numerically calculating spin and charge gaps using the density-matrix renormalization group.