Improved stability regions for ground states of the extended Hubbard model

The ground state phase diagram of the extended Hubbard model containing nearest and next-to-nearest neighbor interactions is investigated in the thermodynamic limit using an exact method. It is found that taking into account local correlations and adding next-to-nearest neighbor interactions both have significant effects on the position of the phase boundaries. Improved stability domains for the $\eta$-pairing state and for the fully saturated ferromagnetic state at half filling have been constructed. The results show that these states are the ground states for model Hamiltonians with realistic values of the interaction parameters.Comment: 21 pages (10 figures are included) Revtex, revised version. To be published in Phys. Rev. B. E-mail: [email protected]

Superconductivity in the Two-Band Hubbard Model in Infinite Dimensions

We study a two-band Hubbard model in the limit of infinite dimensions, using a combination of analytical methods and Monte-Carlo techniques. The normal state is found to display various metal to insulators transitions as a function of doping and interaction strength. We derive self-consistent equations for the local Green's functions in the presence of superconducting long-range order, and extend previous algorithms to this case. We present direct numerical evidence that in a specific range of parameter space, the normal state is unstable against a superconducting state characterized by a strongly frequency dependent order-parameter.Comment: 12 pages (14 figures not included, available upon request), Latex, LPTENS Preprint 93/1

Ferromagnetism in Correlated Electron Systems: Generalization of Nagaoka's Theorem

Nagaoka's theorem on ferromagnetism in the Hubbard model with one electron less than half filling is generalized to the case where all possible nearest-neighbor Coulomb interactions (the density-density interaction $V$, bond-charge interaction $X$, exchange interaction $F$, and hopping of double occupancies $F'$) are included. It is shown that for ferromagnetic exchange coupling ($F>0$) ground states with maximum spin are stable already at finite Hubbard interaction $U>U_c$. For non-bipartite lattices this requires a hopping amplitude $t\leq0$. For vanishing $F$ one obtains $U_c\to\infty$ as in Nagaoka's theorem. This shows that the exchange interaction $F$ is important for stabilizing ferromagnetism at finite $U$. Only in the special case $X=t$ the ferromagnetic state is stable even for $F=0$, provided the lattice allows the hole to move around loops.Comment: 13 pages, uuencoded postscript, includes 1 table and 2 figure

Magnetic phase diagram of the Hubbard model

The competition between commensurate and incommensurate spin-density-wave phases in the infinite-dimensional single-band Hubbard model is examined with quantum Monte Carlo simulation and strong and weak coupling approximations. Quantum fluctuations modify the weak-coupling phase diagram by factors of order unity and produce remarkable agreement with the quantum Monte Carlo data, but strong-coupling theories (that map onto effective Falicov-Kimball models) display pathological behavior. The single-band model can be used to describe much of the experimental data in Cr and its dilute alloys with V and Mn.Comment: 12 pages plus 3 uuencoded postscript figures, ReVTe

A Quantum Monte Carlo algorithm for non-local corrections to the Dynamical Mean-Field Approximation

We present the algorithmic details of the dynamical cluster approximation (DCA), with a quantum Monte Carlo (QMC) method used to solve the effective cluster problem. The DCA is a fully-causal approach which systematically restores non-local correlations to the dynamical mean field approximation (DMFA) while preserving the lattice symmetries. The DCA becomes exact for an infinite cluster size, while reducing to the DMFA for a cluster size of unity. We present a generalization of the Hirsch-Fye QMC algorithm for the solution of the embedded cluster problem. We use the two-dimensional Hubbard model to illustrate the performance of the DCA technique. At half-filling, we show that the DCA drives the spurious finite-temperature antiferromagnetic transition found in the DMFA slowly towards zero temperature as the cluster size increases, in conformity with the Mermin-Wagner theorem. Moreover, we find that there is a finite temperature metal to insulator transition which persists into the weak-coupling regime. This suggests that the magnetism of the model is Heisenberg like for all non-zero interactions. Away from half-filling, we find that the sign problem that arises in QMC simulations is significantly less severe in the context of DCA. Hence, we were able to obtain good statistics for small clusters. For these clusters, the DCA results show evidence of non-Fermi liquid behavior and superconductivity near half-filling.Comment: 25 pages, 15 figure

Self-Consistent Second Order Perturbation Theory for the Hubbard Model in Two Dimensions

We apply self-consistent second order perturbation theory (SCSOPT) with respect to the on-site repulsive interaction U to study the Hubbard model in two dimensions. We investigate single particle properties of the model over the entire doping range at zero temperature. It is shown that as doping decreases toward half-filling $\omega$-mass enhancement factor increases, while k-mass enhancement factor decreases. The increase in $\omega$-mass enhancement factor is larger than the decrease in k-mass enhancement factor, so that total-mass is larger than that in the non-interacting case. When particle number density per unit cell n is given by 0.64<n<1.0 interaction enhances anisotropy of the Fermi surface, whereas at lower densities n<0.64 interaction suppresses anisotropy of it. Due to the decrease in k-mass enhancement factor the density of states (DOS) at the Fermi level is suppressed. It is possible to understand the results within the framework of the weak coupling Fermi liquid theory.Comment: 8 pages, 12 embedded EPS figures, to appear in J. Phys. Soc. Jpn. Vol. 68-3 (1999

Symmetry breaking in the Hubbard model at weak coupling

The phase diagram of the Hubbard model is studied at weak coupling in two and three spatial dimensions. It is shown that the Neel temperature and the order parameter in d=3 are smaller than the Hartree-Fock predictions by a factor of q=0.2599. For d=2 we show that the self-consistent (sc) perturbation series bears no relevance to the behavior of the exact solution of the Hubbard model in the symmetry-broken phase. We also investigate an anisotropic model and show that the coupling between planes is essential for the validity of mean-field-type order parameters

Metallic ferromagnetism: Progress in our understanding of an old strong-coupling problem

Metallic ferromagnetism is in general an intermediate to strong coupling phenomenon. Since there do not exist systematic analytic methods to investigate such types of problems, the microscopic origin of metallic ferromagnetism is still not sufficiently understood. However, during the last two or three years remarkable progress was made in this field: It is now certain that even in the one-band Hubbard model metallic ferromagnetism is stable in dimensions $d=1,$ 2, and $\infty$ on regular lattices and at intermediate values of the interaction $U$ and density $n$. In this paper the basic questions and recent insights regarding the microscopic conditions favoring metallic ferromagnetism in this model are reviewed. These findings are contrasted with the results for the orbitally degenerate case.Comment: 16 pages, 13 figures, latex using vieweg.sty (enclosed); typos corrected; to appear in "Advances in Solid State Physics", Vol. 3

Vertex-corrected perturbation theory for the electron-phonon problem with non-constant density of states

A series of weak-coupling perturbation theories which include the lowest-order vertex corrections are applied to the attractive Holstein model in infinite dimensions. The approximations are chosen to reproduce the iterated perturbation theory in the limit of half-filling and large phonon frequency (where the Holstein model maps onto the Hubbard model). Comparison is made with quantum Monte Carlo solutions to test the accuracy of different approximation schemes.Comment: 31 pages, 15 figures, typeset in ReVTe

Ferromagnetism in the one-dimensional Hubbard model with orbital degeneracy: From low to high electron density

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) electron density when the interactions are sufficiently strong. Quasi-long-range order of triplet superconductivity coexists with the ferromagnetic order for a strong Hund coupling region, where the inter-orbital interaction U'-J is attractive. At quarter-filling (n=1), the insulating ferromagnetic state appears accompanying orbital quasi-long-range order. For low densities (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), the phase diagram of the ferromagnetic phase is similar to that obtained in infinite dimensions. In this case, the double exchange mechanism is operative to stabilize 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<n<1.75 and phase separation occurs for n just below the half-filling (n=2).Comment: 16 pages, 16 figures, final version, references adde