333 research outputs found
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 -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 ,
bond-charge interaction , exchange interaction , and hopping of double
occupancies ) are included. It is shown that for ferromagnetic exchange
coupling () ground states with maximum spin are stable already at finite
Hubbard interaction . For non-bipartite lattices this requires a hopping
amplitude . For vanishing one obtains as in
Nagaoka's theorem. This shows that the exchange interaction is important
for stabilizing ferromagnetism at finite . Only in the special case
the ferromagnetic state is stable even for , 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 -mass enhancement factor increases, while k-mass
enhancement factor decreases. The increase in -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
2, and on regular lattices and at intermediate values of the
interaction and density . 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
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