723 research outputs found
A Variational Estimate of the Binding Energy of Charge-Transfer Excitons in the Cuprate Superconductors.
We present a variational estimate for the binding energy of a Frenkel exciton
in the insulating cuprate superconductors. Starting from the three band Hubbard
model we perform a canonical transformation to O(), where is the bare
nearest neighbour copper-oxygen hopping integral. An effective Hamiltonian is
then derived to describe the hopping of the exciton through the copper oxide
plane. The critical parameter in the model is the nearest neighbour
copper-oxygen coulomb repulsion, . It is found that a critical value of
is needed to observe bound Frenkel excitons, and that these excitons have the
same symmetry as the parent copper orbital, . We determine the
critical value of using a variational approach, and attempt to fit the
parameters of the model to known experimental results.Comment: Latex document. Figures on request
A renormalisation-group approach to two-body scattering with long-range forces
We apply the renormalisation-group to two-body scattering by a combination of
known long-range and unknown short-range forces. A crucial feature is that the
low-energy effective theory is regulated by applying a cut-off in the basis of
distorted waves for the long range potential. We illustrate the method by
applying it to scattering in the presence of a repulsive 1/r^2 potential. We
find a trivial fixed point, describing systems with weak short-range
interactions, and a unstable fixed point. The expansion around the latter
corresponds to a distorted-wave effective-range expansion.Comment: 4 pages (AIP style), talk presented at Mesons and Light Nuclei,
Prague, 200
Quantized Lattice Dynamic Effects on the Spin-Peierls Transition
The density matrix renormalization group method is used to investigate the
spin-Peierls transition for Heisenberg spins coupled to quantized phonons. We
use a phonon spectrum that interpolates between a gapped, dispersionless
(Einstein) limit to a gapless, dispersive (Debye) limit. A variety of
theoretical probes are used to determine the quantum phase transition,
including energy gap crossing, a finite size scaling analysis, bond order
auto-correlation functions, and bipartite quantum entanglement. All these
probes indicate that in the antiadiabatic phonon limit a quantum phase
transition of the Berezinskii-Kosterlitz-Thouless type is observed at a
non-zero spin-phonon coupling, . An extrapolation from the
Einstein limit to the Debye limit is accompanied by an increase in for a fixed optical () phonon gap. We therefore conclude that the
dimerized ground state is more unstable with respect to Debye phonons, with the
introduction of phonon dispersion renormalizing the effective spin-lattice
coupling for the Peierls-active mode. We also show that the staggered spin-spin
and phonon displacement order parameters are unreliable means of determining
the transition.Comment: To be published in Phys. Rev.
Screening and the quantitative π-model description of the optical spectra and polarizations of phenyl based oligomers
The long standing problem of the inability of many semiempirical models to correctly predict the polarization of the higher dipole allowed optical transitions of phenyl based π-conjugated polymers and molecules is examined and related to the issue of internal and external screening of π-π electron Coulomb interactions within the molecules. Following a review of previous theoretical and experimental work, π electron only the Complete Neglect of Differential Overlap (CNDO) model is presented which, for the first time, is able to predict accurately the energies and symmetries of all the observed optical transitions of benzene, biphenyl and trans -stilbene, up to ~8-10 eV. In so doing, it is demonstrated that the problem with previous calculations was the noninclusion of screening from outside the p electron system itself. By fitting separately the spectra in hydrocarbon based condensed phases, in the gas phase and in solid rare gas matrices, and comparing the resulting model parameters, we show that, while the effects of screening from the environment are certainly noticeable, the most important spectral features - in particular the ordering of dipole allowed transitions - come from effective screening by the s electrons. We find that both of these effects can be adequately accounted for within a π electron only model by using a dielectric constant and appropriate parameter renormalization
Peierls transition in the quantum spin-Peierls model
We use the density matrix renormalization group method to investigate the
role of longitudinal quantized phonons on the Peierls transition in the
spin-Peierls model. For both the XY and Heisenberg spin-Peierls model we show
that the staggered phonon order parameter scales as (and the
dimerized bond order scales as ) as (where
is the electron-phonon interaction). This result is true for both linear and
cyclic chains. Thus, we conclude that the Peierls transition occurs at
in these models. Moreover, for the XY spin-Peierls model we show
that the quantum predictions for the bond order follow the classical prediction
as a function of inverse chain size for small . We therefore conclude
that the zero phase transition is of the mean-field type
Flux front penetration in disordered superconductors
We investigate flux front penetration in a disordered type II superconductor
by molecular dynamics (MD) simulations of interacting vortices and find scaling
laws for the front position and the density profile. The scaling can be
understood performing a coarse graining of the system and writing a disordered
non-linear diffusion equation. Integrating numerically the equation, we observe
a crossover from flat to fractal front penetration as the system parameters are
varied. The value of the fractal dimension indicates that the invasion process
is described by gradient percolation.Comment: 5 pages, 4 figures, to appear in Phys. Rev. Let
Effective theories of scattering with an attractive inverse-square potential and the three-body problem
A distorted-wave version of the renormalisation group is applied to
scattering by an inverse-square potential and to three-body systems. In
attractive three-body systems, the short-distance wave function satisfies a
Schroedinger equation with an attractive inverse-square potential, as shown by
Efimov. The resulting oscillatory behaviour controls the renormalisation of the
three-body interactions, with the renormalisation-group flow tending to a limit
cycle as the cut-off is lowered. The approach used here leads to single-valued
potentials with discontinuities as the bound states are cut off. The
perturbations around the cycle start with a marginal term whose effect is
simply to change the phase of the short-distance oscillations, or the
self-adjoint extension of the singular Hamiltonian. The full power counting in
terms of the energy and two-body scattering length is constructed for
short-range three-body forces.Comment: 19 pages (RevTeX), 2 figure
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