1,749 research outputs found
Optical conductivity of a metal-insulator transition for the Anderson-Hubbard model in 3 dimensions away from 1/2 filling
We have completed a numerical investigation of the Anderson-Hubbard model for
three-dimensional simple cubic lattices using a real-space self-consistent
Hartree-Fock decoupling approximation for the Hubbard interaction. In this
formulation we treat the spatial disorder exactly, and therefore we account for
effects arising from localization physics. We have examined the model for
electronic densities well away 1/2 filling, thereby avoiding the physics of a
Mott insulator. Several recent studies have made clear that the combined
effects of electronic interactions and spatial disorder can give rise to a
suppression of the electronic density of states, and a subsequent
metal-insulator transition can occur. We augment such studies by calculating
the ac conductivity for such systems. Our numerical results show that weak
interactions enhance the density of states at the Fermi level and the
low-frequency conductivity, there are no local magnetic moments, and the ac
conductivity is Drude-like. However, with a large enough disorder strength and
larger interactions the density of states at the Fermi level and the
low-frequency conductivity are both suppressed, the conductivity becomes
non-Drude-like, and these phenomena are accompanied by the presence of local
magnetic moments. The low-frequency conductivity changes from a sigma-sigma_dc
omega^{1/2} behaviour in the metallic phase, to a sigma omega^2 behaviour in
the nonmetallic regime. Our numerical results show that the formation of
magnetic moments is essential to the suppression of the density of states at
the Fermi level, and therefore essential to the metal-insulator transition
Dynamical properties of the single--hole -- model on a 32--site square lattice
We present results of an exact diagonalization calculation of the spectral
function for a single hole described by the -- model
propagating on a 32--site square cluster. The minimum energy state is found at
a crystal momentum , consistent with
theory, and our measured dispersion relation agrees well with that determined
using the self--consistent Born approximation. In contrast to smaller cluster
studies, our spectra show no evidence of string resonances. We also make a
qualitative comparison of the variation of the spectral weight in various
regions of the first Brillouin zone with recent ARPES data.Comment: 10 pages, 5 postscript figures include
Critiquing Variational Theories of the Anderson-Hubbard Model: Real-Space Self-Consistent Hartree-Fock Solutions
A simple and commonly employed approximate technique with which one can
examine spatially disordered systems when strong electronic correlations are
present is based on the use of real-space unrestricted self-consistent
Hartree-Fock wave functions. In such an approach the disorder is treated
exactly while the correlations are treated approximately. In this report we
critique the success of this approximation by making comparisons between such
solutions and the exact wave functions for the Anderson-Hubbard model. Due to
the sizes of the complete Hilbert spaces for these problems, the comparisons
are restricted to small one-dimensional chains, up to ten sites, and a 4x4
two-dimensional cluster, and at 1/2 filling these Hilbert spaces contain about
63,500 and 166 million states, respectively. We have completed these
calculations both at and away from 1/2 filling. This approximation is based on
a variational approach which minimizes the Hartree-Fock energy, and we have
completed comparisons of the exact and Hartree-Fock energies. However, in order
to assess the success of this approximation in reproducing ground-state
correlations we have completed comparisons of the local charge and spin
correlations, including the calculation of the overlap of the Hartree-Fock wave
functions with those of the exact solutions. We find that this approximation
reproduces the local charge densities to quite a high accuracy, but that the
local spin correlations, as represented by , are not as well
represented. In addition to these comparisons, we discuss the properties of the
spin degrees of freedom in the HF approximation, and where in the
disorder-interaction phase diagram such physics may be important
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An Exact Diagonalization Demonstration of Incommensurability and Rigid Band Filling for N Holes in the t-J Model
We have calculated S(q) and the single particle distribution function
for N holes in the t - J model on a non--square sqrt{8} X sqrt{32} 16--site
lattice with periodic boundary conditions; we justify the use of this lattice
in compariosn to those of having the full square symmetry of the bulk. This new
cluster has a high density of vec k points along the diagonal of reciprocal
space, viz. along k = (k,k). The results clearly demonstrate that when the
single hole problem has a ground state with a system momentum of vec k =
(pi/2,pi/2), the resulting ground state for N holes involves a shift of the
peak of the system's structure factor away from the antiferromagnetic state.
This shift effectively increases continuously with N. When the single hole
problem has a ground state with a momentum that is not equal to k =
(pi/2,pi/2), then the above--mentioned incommensurability for N holes is not
found. The results for the incommensurate ground states can be understood in
terms of rigid--band filling: the effective occupation of the single hole k =
(pi/2,pi/2) states is demonstrated by the evaluation of the single particle
momentum distribution function . Unlike many previous studies, we show
that for the many hole ground state the occupied momentum states are indeed k =
(+/- pi/2,+/- pi/2) states.Comment: Revtex 3.0; 23 pages, 1 table, and 13 figures, all include
On the contrasting spin dynamics of , and near half filling
We present simple calculations which show that incommensurability upon doping
and the width of the magnetically ordered phase in Mott-Hubbard insulators
depend strongly on the location of the hole/electron pockets in the Brillouin
zone. For systems, we found the pockets at ,
in which case the corrections to the antiferromagnetic spin stiffness grow with
doping and destroy the commensurate antiferromagnetic ordering already at a
very small doping. On the other hand, in , the hole pockets are
located at and the symmetry related points, in which case the
corrections to the stiffness scale linearly with the density of carriers and do
not destroy commensurate spin ordering. For , systems the situation is
less certain, but our results favor hole pockets at . We also
discuss briefly the tendency towards phase separation.Comment: 18 pages, LaTe
Enhanced Bound State Formation in Two Dimensions via Stripe-Like Hopping Anisotropies
We have investigated two-electron bound state formation in a square
two-dimensional t-J-U model with hopping anisotropies for zero electron
density; these anisotropies are introduced to mimic the hopping energies
similar to those expected in stripe-like arrangements of holes and spins found
in various transition metal oxides. In this report we provide analytical
solutions to this problem, and thus demonstrate that bound-state formation
occurs at a critical exchange coupling, J_c, that decreases to zero in the
limit of extreme hopping anisotropy t_y/t_x -> 0. This result should be
contrasted with J_c/t = 2 for either a one-dimensional chain, or a
two-dimensional plane with isotropic hopping. Most importantly, this behaviour
is found to be qualitatively similar to that of two electrons on the two-leg
ladder problem in the limit of t_interchain/t_intrachain -> 0. Using the latter
result as guidance, we have evaluated the pair correlation function, thus
determining that the bound state corresponds to one electron moving along one
chain, with the second electron moving along the opposite chain, similar to two
electrons confined to move along parallel, neighbouring, metallic stripes. We
emphasize that the above results are not restricted to the zero density limit -
we have completed an exact diagonalization study of two holes in a 12 X 2
two-leg ladder described by the t-J model and have found that the
above-mentioned lowering of the binding energy with hopping anisotropy persists
near half filling.Comment: 6 pages, 3 eps figure
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Spin and Charge Texture around In-Plane Charge Centers in the CuO_2 planes
Recent experiments on La_2Cu_{1-x}Li_xO_4 show that although the doped holes
remain localized near the substitutional Li impurities, magnetic order is
rapidly suppressed. An examination of the spin texture around a bound hole in a
CuO_2 plane shows that the formation of a skyrmion is favored in a wide range
of parameters, as was previously proposed in the context of Sr doping. The spin
texture may be observable by elastic diffuse neutron scattering, and may also
have a considerable effect on NMR lineshapes.Comment: 4 pages, postscript file, hardcopy available upon request, to appear
in PR
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