923 research outputs found
Variational cluster approach to correlated electron systems in low dimensions
A self-energy-functional approach is applied to construct cluster
approximations for correlated lattice models. It turns out that the
cluster-perturbation theory (Senechal et al, PRL 84, 522 (2000)) and the
cellular dynamical mean-field theory (Kotliar et al, PRL 87, 186401 (2001)) are
limiting cases of a more general cluster method. Results for the
one-dimensional Hubbard model are discussed with regard to boundary conditions,
bath degrees of freedom and cluster size.Comment: 4 pages, final version with minor change
Mott transition in one dimension: Benchmarking dynamical cluster approaches
The variational cluster approach (VCA) is applied to the one-dimensional
Hubbard model at zero temperature using clusters (chains) of up to ten sites
with full diagonalization and the Lanczos method as cluster solver. Within the
framework of the self-energy-functional theory (SFT), different cluster
reference systems with and without bath degrees of freedom, in different
topologies and with different sets of variational parameters are considered.
Static and one-particle dynamical quantities are calculated for half-filling as
a function of U as well as for fixed U as a function of the chemical potential
to study the interaction- and filling-dependent metal-insulator (Mott)
transition. The recently developed Q-matrix technique is used to compute the
SFT grand potential. For benchmarking purposes we compare the VCA results with
exact results available from the Bethe ansatz, with essentially exact dynamical
DMRG data, with (cellular) dynamical mean-field theory and full diagonalization
of isolated Hubbard chains. Several issues are discussed including convergence
of the results with cluster size, the ability of cluster approaches to access
the critical regime of the Mott transition, efficiency in the optimization of
correlated-site vs. bath-site parameters and of multi-dimensional parameter
optimization. We also study the role of bath sites for the description of
excitation properties and as charge reservoirs for the description of filling
dependencies. The VCA turns out to be a computationally cheap method which is
competitive with established cluster approaches.Comment: 19 pages, 19 figures, v3 with minor corrections, extended discussio
Continuity of affine transformations of white noise test functionals and applications
Translations and scalings defined on the Schwartz space of tempered distributions induce continuous transformations on the space of white noise test functionals [25]. Continuity of the induced transformations with respect to their parameters is proved. As a consequence one obtains a direct simple proof of the fact that the space of white noise test functionals is infinitely differentiable in Fréchet sense. Moreover, it is shown that the Wiener semigroup acts as a mollifier on the space of test functionals. © 1992
Influence of uncorrelated overlayers on the magnetism in thin itinerant-electron films
The influence of uncorrelated (nonmagnetic) overlayers on the magnetic
properties of thin itinerant-electron films is investigated within the
single-band Hubbard model. The Coulomb correlation between the electrons in the
ferromagnetic layers is treated by using the spectral density approach (SDA).
It is found that the presence of nonmagnetic layers has a strong effect on the
magnetic properties of thin films. The Curie temperatures of very thin films
are modified by the uncorrelated overlayers. The quasiparticle density of
states is used to analyze the results. In addition, the coupling between the
ferromagnetic layers and the nonmagnetic layers is discussed in detail. The
coupling depends on the band occupation of the nonmagnetic layers, while it is
almost independent of the number of the nonmagnetic layers. The induced
polarization in the nonmagnetic layers shows a long-range decreasing
oscillatory behavior and it depends on the coupling between ferromagnetic and
nonmagnetic layers.Comment: 9 pages, RevTex, 6 figures, for related work see:
http://orion.physik.hu-berlin.d
Theory of Spin-Resolved Auger-Electron Spectroscopy from Ferromagnetic 3d-Transition Metals
CVV Auger electron spectra are calculated for a multi-band Hubbard model
including correlations among the valence electrons as well as correlations
between core and valence electrons. The interest is focused on the
ferromagnetic 3d-transition metals. The Auger line shape is calculated from a
three-particle Green function. A realistic one-particle input is taken from
tight-binding band-structure calculations. Within a diagrammatic approach we
can distinguish between the \textit{direct} correlations among those electrons
participating in the Auger process and the \textit{indirect} correlations in
the rest system. The indirect correlations are treated within second-order
perturbation theory for the self-energy. The direct correlations are treated
using the valence-valence ladder approximation and the first-order perturbation
theory with respect to valence-valence and core-valence interactions. The
theory is evaluated numerically for ferromagnetic Ni. We discuss the
spin-resolved quasi-particle band structure and the Auger spectra and
investigate the influence of the core hole.Comment: LaTeX, 12 pages, 8 eps figures included, Phys. Rev. B (in press
Two-site dynamical mean-field theory
It is shown that a minimum realization of the dynamical mean-field theory
(DMFT) can be achieved by mapping a correlated lattice model onto an impurity
model in which the impurity is coupled to an uncorrelated bath that consists of
a single site only. The two-site impurity model can be solved exactly. The
mapping is approximate. The self-consistency conditions are constructed in a
way that the resulting ``two-site DMFT'' reduces to the previously discussed
linearized DMFT for the Mott transition. It is demonstrated that a reasonable
description of the mean-field physics is possible with a minimum computational
effort. This qualifies the simple two-site DMFT for a systematic study of more
complex lattice models which cannot be treated by the full DMFT in a feasible
way. To show the strengths and limitations of the new approach, the single-band
Hubbard model is investigated in detail. The predictions of the two-site DMFT
are compared with results of the full DMFT. Internal consistency checks are
performed which concern the Luttinger sum rule, other Fermi-liquid relations
and thermodynamic consistency.Comment: LaTeX, 14 pages, 8 eps figures included, Phys. Rev. B (in press
Charge ordering in extended Hubbard models: Variational cluster approach
We present a generalization of the recently proposed variational cluster
perturbation theory to extended Hubbard models at half filling with repulsive
nearest neighbor interaction. The method takes into account short-range
correlations correctly by the exact diagonalisation of clusters of finite size,
whereas long-range order beyond the size of the clusters is treated on a
mean-field level. For one dimension, we show that quantum Monte Carlo and
density-matrix renormalization-group results can be reproduced with very good
accuracy. Moreover we apply the method to the two-dimensional extended Hubbard
model on a square lattice. In contrast to the one-dimensional case, a first
order phase transition between spin density wave phase and charge density wave
phase is found as function of the nearest-neighbor interaction at onsite
interactions U>=3t. The single-particle spectral function is calculated for
both the one-dimensional and the two-dimensional system.Comment: 15 pages, 12 figure
Dynamical mean-field theory of indirect magnetic exchange
To analyze the physical properties arising from indirect magnetic exchange
between several magnetic adatoms and between complex magnetic nanostructures on
metallic surfaces, the real-space extension of dynamical mean-field theory
(R-DMFT) appears attractive as it can be applied to systems of almost arbitrary
geometry and complexity. While R-DMFT describes the Kondo effect of a single
adatom exactly, indirect magnetic (RKKY) exchange is taken into account on an
approximate level only. Here, we consider a simplified model system consisting
of two magnetic Hubbard sites ("adatoms") hybridizing with a non-interacting
tight-binding chain ("substrate surface"). This two-impurity Anderson model
incorporates the competition between the Kondo effect and indirect exchange but
is amenable to an exact numerical solution via the density-matrix
renormalization group (DMRG). The particle-hole symmetric model at half-filling
and zero temperature is used to benchmark R-DMFT results for the magnetic
coupling between the two adatoms and for the magnetic properties induced in the
substrate. In particular, the dependence of the local adatom and the nonlocal
adatom-adatom static susceptibilities as well as the magnetic response of the
substrate on the distance between the adatoms and on the strength of their
coupling with the substrate is studied. We find both, excellent agreement with
the DMRG data even on subtle details of the competition between RKKY exchange
and the Kondo effect but also complete failure of the R-DMFT, depending on the
parameter regime considered. R-DMFT calculations are performed using the
Lanczos method as impurity solver. With the real-space extension of the
two-site DMFT, we also benchmark a simplified R-DMFT variant.Comment: 14 pages, 8 figure
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