5,140 research outputs found
Local Electronic Correlation at the Two-Particle Level
Electronic correlated systems are often well described by dynamical mean
field theory (DMFT). While DMFT studies have mainly focused hitherto on
one-particle properties, valuable information is also enclosed into local
two-particle Green's functions and vertices. They represent the main ingredient
to compute momentum-dependent response functions at the DMFT level and to treat
non-local spatial correlations at all length scales by means of diagrammatic
extensions of DMFT. The aim of this paper is to present a DMFT analysis of the
local reducible and irreducible two-particle vertex functions for the Hubbard
model in the context of an unified diagrammatic formalism. An interpretation of
the observed frequency structures is also given in terms of perturbation
theory, of the comparison with the atomic limit, and of the mapping onto the
attractive Hubbard model.Comment: 29 pages, 26 Figures. Accepted for publication in Phys. Rev.
Symmetry classification of energy bands in graphene and silicene
We present the results of the symmetry classification of the electron energy
bands in graphene and silicene using group theory algebra and the
tight--binding approximation. The analysis is performed both in the absence and
in the presence of the spin-orbit coupling. We also discuss the bands merging
in the Brillouin zone symmetry points and the conditions for the latter to
become Dirac points.Comment: LaTeX, 6 pages, 2 eps Figures. A Figure and a citation were added.
Accepted for publication in Graphen
Self-consistent Green's functions formalism with three-body interactions
We extend the self-consistent Green's functions formalism to take into
account three-body interactions. We analyze the perturbative expansion in terms
of Feynman diagrams and define effective one- and two-body interactions, which
allows for a substantial reduction of the number of diagrams. The procedure can
be taken as a generalization of the normal ordering of the Hamiltonian to fully
correlated density matrices. We give examples up to third order in perturbation
theory. To define nonperturbative approximations, we extend the equation of
motion method in the presence of three-body interactions. We propose schemes
that can provide nonperturbative resummation of three-body interactions. We
also discuss two different extensions of the Koltun sum rule to compute the
ground state of a many-body system.Comment: 26 pages, 19 figure
Best possible rates of distribution of dense lattice orbits in homogeneous spaces
The present paper establishes upper and lower bounds on the speed of
approximation in a wide range of natural Diophantine approximation problems.
The upper and lower bounds coincide in many cases, giving rise to optimal
results in Diophantine approximation which were inaccessible previously. Our
approach proceeds by establishing, more generally, upper and lower bounds for
the rate of distribution of dense orbits of a lattice subgroup in a
connected Lie (or algebraic) group , acting on suitable homogeneous spaces
. The upper bound is derived using a quantitative duality principle for
homogeneous spaces, reducing it to a rate of convergence in the mean ergodic
theorem for a family of averaging operators supported on and acting on
. In particular, the quality of the upper bound on the rate of
distribution we obtain is determined explicitly by the spectrum of in the
automorphic representation on . We show that the rate
is best possible when the representation in question is tempered, and show that
the latter condition holds in a wide range of examples
Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua
We study marginal and relevant supersymmetric deformations of the N=4
super-Yang-Mills theory in four dimensions. Our primary innovation is the
interpretation of the moduli spaces of vacua of these theories as
non-commutative spaces. The construction of these spaces relies on the
representation theory of the related quantum algebras, which are obtained from
F-term constraints. These field theories are dual to superstring theories
propagating on deformations of the AdS_5xS^5 geometry. We study D-branes
propagating in these vacua and introduce the appropriate notion of algebraic
geometry for non-commutative spaces. The resulting moduli spaces of D-branes
have several novel features. In particular, they may be interpreted as
symmetric products of non-commutative spaces. We show how mirror symmetry
between these deformed geometries and orbifold theories follows from T-duality.
Many features of the dual closed string theory may be identified within the
non-commutative algebra. In particular, we make progress towards understanding
the K-theory necessary for backgrounds where the Neveu-Schwarz antisymmetric
tensor of the string is turned on, and we shed light on some aspects of
discrete anomalies based on the non-commutative geometry.Comment: 60 pages, 4 figures, JHEP format, amsfonts, amssymb, amsmat
Stability of self-consistent solutions for the Hubbard model at intermediate and strong coupling
We present a general framework how to investigate stability of solutions
within a single self-consistent renormalization scheme being a parquet-type
extension of the Baym-Kadanoff construction of conserving approximations. To
obtain a consistent description of one- and two-particle quantities, needed for
the stability analysis, we impose equations of motion on the one- as well on
the two-particle Green functions simultaneously and introduce approximations in
their input, the completely irreducible two-particle vertex. Thereby we do not
loose singularities caused by multiple two-particle scatterings. We find a
complete set of stability criteria and show that each instability, singularity
in a two-particle function, is connected with a symmetry-breaking order
parameter, either of density type or anomalous. We explicitly study the Hubbard
model at intermediate coupling and demonstrate that approximations with static
vertices get unstable before a long-range order or a metal-insulator transition
can be reached. We use the parquet approximation and turn it to a workable
scheme with dynamical vertex corrections. We derive a qualitatively new theory
with two-particle self-consistence, the complexity of which is comparable with
FLEX-type approximations. We show that it is the simplest consistent and stable
theory being able to describe qualitatively correctly quantum critical points
and the transition from weak to strong coupling in correlated electron systems.Comment: REVTeX, 26 pages, 12 PS figure
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