280 research outputs found
Application of the Density Matrix Renormalization Group in momentum space
We investigate the application of the Density Matrix Renormalization Group
(DMRG) to the Hubbard model in momentum-space. We treat the one-dimensional
models with dispersion relations corresponding to nearest-neighbor hopping and
hopping and the two-dimensional model with isotropic nearest-neighbor
hopping. By comparing with the exact solutions for both one-dimensional models
and with exact diagonalization in two dimensions, we first investigate the
convergence of the ground-state energy. We find variational convergence of the
energy with the number of states kept for all models and parameter sets. In
contrast to the real-space algorithm, the accuracy becomes rapidly worse with
increasing interaction and is not significantly better at half filling. We
compare the results for different dispersion relations at fixed interaction
strength over bandwidth and find that extending the range of the hopping in one
dimension has little effect, but that changing the dimensionality from one to
two leads to lower accuracy at weak to moderate interaction strength. In the
one-dimensional models at half-filling, we also investigate the behavior of the
single-particle gap, the dispersion of spinon excitations, and the momentum
distribution function. For the single-particle gap, we find that proper
extrapolation in the number of states kept is important. For the spinon
dispersion, we find that good agreement with the exact forms can be achieved at
weak coupling if the large momentum-dependent finite-size effects are taken
into account for nearest-neighbor hopping. For the momentum distribution, we
compare with various weak-coupling and strong-coupling approximations and
discuss the importance of finite-size effects as well as the accuracy of the
DMRG.Comment: 15 pages, 11 eps figures, revtex
Ground-state energy and spin in disordered quantum dots
We investigate the ground-state energy and spin of disordered quantum dots
using spin-density-functional theory. Fluctuations of addition energies
(Coulomb-blockade peak spacings) do not scale with average addition energy but
remain proportional to level spacing. With increasing interaction strength, the
even-odd alternation of addition energies disappears, and the probability of
non-minimal spin increases, but never exceeds 50%. Within a two-orbital model,
we show that the off-diagonal Coulomb matrix elements help stabilize a ground
state of minimal spin.Comment: 10 pages, 2 figure
Expansion algorithm for the density matrix
A purification algorithm for expanding the single-particle density matrix in
terms of the Hamiltonian operator is proposed. The scheme works with a
predefined occupation and requires less than half the number of matrix-matrix
multiplications compared to existing methods at low (90%)
occupancy. The expansion can be used with a fixed chemical potential in which
case it is an asymmetric generalization of and a substantial improvement over
grand canonical McWeeny purification. It is shown that the computational
complexity, measured as number of matrix multiplications, essentially is
independent of system size even for metallic materials with a vanishing band
gap.Comment: 5 pages, 4 figures, to appear in Phys. Rev.
Theoretical investigations of a highly mismatched interface: the case of SiC/Si(001)
Using first principles, classical potentials, and elasticity theory, we
investigated the structure of a semiconductor/semiconductor interface with a
high lattice mismatch, SiC/Si(001). Among several tested possible
configurations, a heterostructure with (i) a misfit dislocation network pinned
at the interface and (ii) reconstructed dislocation cores with a carbon
substoichiometry is found to be the most stable one. The importance of the slab
approximation in first-principles calculations is discussed and estimated by
combining classical potential techniques and elasticity theory. For the most
stable configuration, an estimate of the interface energy is given. Finally,
the electronic structure is investigated and discussed in relation with the
dislocation array structure. Interface states, localized in the heterostructure
gap and located on dislocation cores, are identified
Density functional theory of spin-polarized disordered quantum dots
Using density functional theory, we investigate fluctuations of the ground
state energy of spin-polarized, disordered quantum dots in the metallic regime.
To compare to experiment, we evaluate the distribution of addition energies and
find a convolution of the Wigner-Dyson distribution, expected for noniteracting
electrons, with a narrower Gaussian distribution due to interactions. The tird
moment of the total distribution is independent of interactions, and so is
predicted to decrease by a factor of 0.405 upon application of a magnetic field
which transforms from the Gaussian orthogonal to the Gaussian unitary ensemble.Comment: 13 pages, 2 figure
Quantum lattice dynamical effects on the single-particle excitations in 1D Mott and Peierls insulators
As a generic model describing quasi-one-dimensional Mott and Peierls
insulators, we investigate the Holstein-Hubbard model for half-filled bands
using numerical techniques. Combining Lanczos diagonalization with Chebyshev
moment expansion we calculate exactly the photoemission and inverse
photoemission spectra and use these to establish the phase diagram of the
model. While polaronic features emerge only at strong electron-phonon
couplings, pronounced phonon signatures, such as multi-quanta band states, can
be found in the Mott insulating regime as well. In order to corroborate the
Mott to Peierls transition scenario, we determine the spin and charge
excitation gaps by a finite-size scaling analysis based on density-matrix
renormalization group calculations.Comment: 5 pages, 5 figure
Pairing in Cu-O Models: Clues of Joint Electron-Phonon and Electron-Electron Interactions
We discuss a many-electron Hamiltonian with Hubbard-like repulsive
interaction and linear coupling to the phonon branches, having the Cu-O plane
of the superconducting cuprates as a paradigm. A canonical transformation
extracts an effective two-body problem from the many-body theory. As a
prototype system we study the \cu cluster, which yields electronic pairing in
the Hubbard model; moreover, a standard treatment of the Jahn-Teller effect
predicts distortions that destroy electronic pairing. Remarkably, calculations
that keep all the electronic spectrum into account show that vibrations are
likely to be synergic with electronic pairing, if the coupling to
half-breathing modes predominates, as experiments suggest.Comment: 4 pages, 3 figures, accepted by Phys. Rev.
Electromagnetic characteristics of bilayer quantum Hall systems in the presence of interlayer coherence and tunneling
The electromagnetic characteristics of bilayer quantum Hall systems in the
presence of interlayer coherence and tunneling are studied by means of a
pseudospin-texture effective theory and an algebraic framework of the
single-mode approximation, with emphasis on clarifying the nature of the
low-lying neutral collective mode responsible for interlayer tunneling
phenomena. A long-wavelength effective theory, consisting of the collective
mode as well as the cyclotron modes, is constructed. It is seen explicitly from
the electromagnetic response that gauge invariance is kept exact, this
implying, in particular, the absence of the Meissner effect in bilayer systems.
Special emphasis is placed on exploring the advantage of looking into quantum
Hall systems through their response; in particular, subtleties inherent to the
standard Chern-Simons theories are critically examined.Comment: 9 pages, Revtex, to appear in Phys. Rev.
Magnetic phenomena in 5d transition metal nanowires
We have carried out fully relativistic full-potential, spin-polarized,
all-electron density-functional calculations for straight, monatomic nanowires
of the 5d transition and noble metals Os, Ir, Pt and Au. We find that, of these
metal nanowires, Os and Pt have mean-field magnetic moments for values of the
bond length at equilibrium. In the case of Au and Ir, the wires need to be
slightly stretched in order to spin polarize. An analysis of the band
structures of the wires indicate that the superparamagnetic state that our
calculations suggest will affect the conductance through the wires -- though
not by a large amount -- at least in the absence of magnetic domain walls. It
should thus lead to a characteristic temperature- and field dependent
conductance, and may also cause a significant spin polarization of the
transmitted current.Comment: 7 pages, 5 figure
Spin Stiffness of Mesoscopic Quantum Antiferromagnets
We study the spin stiffness of a one-dimensional quantum antiferromagnet in
the whole range of system sizes and temperatures . We show that for
integer and half-odd integer spin case the stiffness differs fundamentally in
its and dependence, and that in the latter case the stiffness exhibits
a striking dependence on the parity of the number of sites. Integer spin chains
are treated in terms of the non-linear sigma model, while half-odd integer spin
chains are discussed in a renormalization group approach leading to a Luttinger
liquid with Aharonov-Bohm type boundary conditions.Comment: 12 pages, LaTe
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