2,671 research outputs found
A self-consistent, conserving theory of the attractive Hubbard model in two dimensions
We have investigated the attractive Hubbard model in the low density limit
for the 2D square lattice using the ladder approximation for the vertex
function in a self-consistent, conserving formulation. In the parameter region
where the on-site attraction is of the order of the bandwidth, we found no
evidence of a pseudo gap. Further, we have observed that the suppression of the
Fermi surface known to destroy superconductivity in one and two dimensions,
when these systems are treated using a non self-consistent theory
(Schmitt-Rink, et al., Phys. Rev. Lett. 63, 445 (1989)), does not occur when
pair-pair interactions are included. However, we do find a quasiparticle
lifetime that varies linearly with temperature, similar to many experiments.
Thus, although this system has a Fermi surface, it shows non Fermi liquid type
behaviour over a wide temperature range. We stress that our work uses thermal
Green's functions along the real time axis, and thus allows for a more accurate
determination of the dynamical properties of a model than theories that require
extrapolations from the imaginary frequency axis.Comment: 13 pages, including 14 figure
Incorporating the Hayflick Limit into a model of Telomere Dynamics
A model of telomere dynamics is proposed and examined. Our model, which
extends a previously introduced two-compartment model that incorporates stem
cells as progenitors of new cells, imposes the Hayflick Limit, the maximum
number of cell divisions that are possible. This new model leads to cell
populations for which the average telomere length is not necessarily a
monotonically decreasing function of time, in contrast to previously published
models. We provide a phase diagram indicating where such results would be
expected. In addition, qualitatively different results are obtained for the
evolution of the total cell population. Last, in comparison to available
leukocyte baboon data, this new model is shown to provide a better fit to
biological data
Magnetic susceptibility of the body-centred orthorhombic LaCuO system
A model Hamiltonian representing the Cu spins in LaCuO in its
low-temperature body-centred orthorhombic phase, that includes both spin-orbit
generated Dzyaloshinskii-Moriya interactions and interplanar exchange, is
examined within the RPA utilizing a Tyablikov decoupling of various high-order
Green's functions. The magnetic susceptibility is evaluated as a function of
temperature and the parameters quantifying these interactions, and compared to
recently obtained experimental data of Lavrov, Ando and collaborators. An
effective Hamiltonian corresponding to a simple tetragonal structure is shown
to reproduce both the magnon spectra and the susceptibility of the more
complicated body-centred orthorhombic model.Comment: 32 pages, 17 figure
Pairing Fluctuations in The Attractive Hubbard Model in the Atomic Limit
BCS theory accounts for the pairing instability in the weak coupling limit,
but fails to describe pairing fluctuations above . One possibility for
describing these fluctuations in the dilute limit is the T-matrix
approximation. We critically examine various degrees of self-consistency in the
T-matrix formalism, along with a non-diagrammatic two-particle self-consistent
(TPSC) formulation, in the strong coupling regime, where an exact solution is
readily available. We find that one particular degree of self-consistency is
quite accurate, particularly at low temperature as evidenced by examining both
static and dynamic properties.Comment: 5 pages, 3 figure
A Comprehensive Dynamical Study of Nucleation and Growth in a One--Dimensional Shear Martensitic Transition
We have constructed a complete hydrodynamic theory of nucleation and growth
in a one--dimensional version of an elastic shear martensitic transformation
with open boundary conditions where we have accounted for interfacial energies
with strain--gradient contributions. We have studied the critical martensitic
nuclei for this problem: Interestingly, the bulk critical nuclei are {\em
twinned} structures, although we have determined that the dominant route for
the formation of martensite is through {\em surface nucleation}. We have
analytically solved for the surface nuclei and evaluated exact nucleation rates
showing the strong preference for surface nucleation. We have also examined the
growth of martensite: There are two possible martensitic growth fronts, {\em
viz}., dynamical twinning and so-called two--kink solutions. These
transformation fronts are separated by a {\em dynamical} phase transition. We
analytically derive this phase diagram and determine expressions for the speeds
of the martensitic growth fronts.Comment: 17 Postscript figures, to appear in Met. Trans
Exact diagonalization analysis of the Anderson-Hubbard model and comparison to real-space self-consistent Hartree-Fock solutions
We have obtained the exact ground state wave functions of the
Anderson-Hubbard model for different electron fillings on a 4x4 lattice with
periodic boundary conditions - for 1/2 filling such ground states have roughly
166 million states. When compared to the uncorrelated ground states (Hubbard
interaction set to zero) we have found strong evidence of the very effective
screening of the charge homogeneities due to the Hubbard interaction. We have
successfully modelled these local charge densities using a non-interacting
model with a static screening of the impurity potentials. In addition, we have
compared such wave functions to self-consistent real-space unrestricted
Hartree-Fock solutions and have found that these approximate ground state wave
functions are remarkably successful at reproducing the local charge densities,
and may indicate the role of dipolar backflow in producing a novel metallic
state in two dimensions
Increasing Superconducting Tc's by a Factor of 1000 with StripeLike Hopping Anisotropies
We have studied the enhancement of the superconducting transition
temperature, Tc, in a t-J-U model of electrons moving on a square lattice in
which anisotropic electronic hopping is introduced. The inclusion of such
hopping mimics, in a approximate fashion, a potentially important
characteristic of materials possessing stripelike charge and spin correlations.
For this model we have calculated Tc for singlet pairing using the non
self-consistent Thouless criterion, and find a dramatic enhancement of Tc
induced by hopping anisotropies. Further, the maximum increase in Tc is
obtained when the system is pushed towards the extreme anisotropy limit, that
is, when the hopping of electrons is confined to occur in 1+0^+ dimensions. We
demonstrate that in this limit the increase in Tc, with respect to the
isotropic system, can be of the order of 1000. We have also determined that in
the extreme anisotropy limit the superconducting gap is an equal mixture of s
and d pairing symmetries (two choices of such a combination being s + d and s +
id) owing to the reduced (square to rectangular) symmetry of the system in the
presence of hopping anisotropies. Thus, the presence of d-wave superconducting
features in materials whose symmetry is very different from that of a
two-dimensional square lattice, with the anisotropy produced by the appearance
of stripes, is not unexpected.Comment: 8 pages (Revtex), 4 eps figure
Examining the metal-to-insulator transitions in Li1+xTi2-xO4 and LiAlyTi2-yO4 with a Quantum Site Percolation model
We have studied the composition-induced metal-to-insulator transitions of
cation substituted Lithium Titanate, in the forms Li1+xTi2-xO4 and
LiAlyTi2-yO4, utilising a quantum site percolation model, and we argue that
such a model provides a very reliable representation of the noninteracting
electrons in this material if strong correlations are ignored. We then
determine whether or not such a model of 3d electrons moving on the Ti
(corner-sharing tetrahedral) sublattice describes the observed
metal-to-insulator transitions, with the critical concentration defined by the
matching of the mobility edge and the chemical potential. Our analysis leads to
quantitative predictions that are in disagreement with those measured
experimentally. For example, experimentally for the LiAlyTi2-yO4 compound an Al
concentration of y_c approximately 0.33 produces a metal-to-insulator
transition, whereas our analysis of a quantum site percolation model predicts
y_c approximately 0.83. One hypothesis that is consistent with these results is
that since strong correlations are ignored in our quantum site percolation
model, which includes the effects of configurational disorder only, such strong
electronic correlations are both present and important.Comment: 5 pages, 4 figure
Theory of Coexisting Transverse Spin Freezing and Long-Ranged Antiferromagnetic Order in Lightly Doped La_{2-x}Sr_x CuO_4
We provide an explanation of the spin-freezing transition recently observed
by Chou et al. (Phys. Rev. Lett. 71, 2323 (1993)) in La_{2-x}Sr_x CuO_4 for x
<= 0.02. We propose that topological excitations of the 2D Heisenberg quantum
antiferromagnet having non-coplanar transverse components have a
pair-interaction energy that qualitatively and quantitatively agrees with the
observed values of spin-freezing temperature as a function of doping.Comment: 18 pages, figures available upon request, revtex, 500
A comprehensive numerical and analytical study of two holes doped into the 2D t-J model
We report on a detailed examination of numerical results and analytical
calculations devoted to a study of two holes doped into a two-dimensional,
square lattice described by the t-J model. Our exact diagonalization numerical
results represent the first solution of the exact ground state of 2 holes in a
32-site lattice. Using this wave function, we have calculated several important
correlation functions, notably the electron momentum distribution function and
the hole-hole spatial correlation function. Further, by studying similar
quantities on smaller lattices, we have managed to perform a finite-size
scaling analysis. We have augmented this work by endeavouring to compare these
results to the predictions of analytical work for two holes moving in an
infinite lattice. This analysis relies on the canonical transformation approach
formulated recently for the t-J model. From this comparison we find excellent
correspondence between our numerical data and our analytical calculations. We
believe that this agreement is an important step helping to justify the
quasiparticle Hamiltonian, and in particular, the quasiparticle interactions,
that result from the canonical transformation approach. Also, the analytical
work allows us to critique the finite-size scaling ansatzes used in our
analysis of the numerical data. One important feature that we can infer from
this successful comparison involves the role of higher harmonics in the
two-particle, d-wave symmetry bound state -- the conventional (\cos(k_x) -
\cos(k_y)) term is only one of many important contributions to the d-wave
symmetry pair wave function.Comment: RevTeX, 25 pages, 15 figures included. One major typo is correcte
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