768 research outputs found
Dynamical Mean-Field Theory - from Quantum Impurity Physics to Lattice Problems
Since the first investigation of the Hubbard model in the limit of infinite
dimensions by Metzner and Vollhardt, dynamical mean-field theory (DMFT) has
become a very powerful tool for the investigation of lattice models of
correlated electrons. In DMFT the lattice model is mapped on an effective
quantum impurity model in a bath which has to be determined self-consistently.
This approach lead to a significant progress in our understanding of typical
correlation problems such as the Mott transition; furthermore, the combination
of DMFT with ab-initio methods now allows for a realistic treatment of
correlated materials. The focus of these lecture notes is on the relation
between quantum impurity physics and the physics of lattice models within DMFT.
Issues such as the observability of impurity quantum phase transitions in the
corresponding lattice models are discussed in detail.Comment: 18 pages, 5 figures, invited paper for the Proceedings of the "3rd
International Summer School on Strongly Correlated Systems, Debrecen, 2004
Numerical Renormalization Group for Impurity Quantum Phase Transitions: Structure of Critical Fixed Points
The numerical renormalization group method is used to investigate zero
temperature phase transitions in quantum impurity systems, in particular in the
particle-hole symmetric soft-gap Anderson model. The model displays two stable
phases whose fixed points can be built up of non-interacting single-particle
states. In contrast, the quantum phase transitions turn out to be described by
interacting fixed points, and their excitations cannot be described in terms of
free particles. We show that the structure of the many-body spectrum of these
critical fixed points can be understood using renormalized perturbation theory
close to certain values of the bath exponents which play the role of critical
dimensions. Contact is made with perturbative renormalization group
calculations for the soft-gap Anderson and Kondo models. A complete description
of the quantum critical many-particle spectra is achieved using suitable
marginal operators; technically this can be understood as epsilon-expansion for
full many-body spectra.Comment: 14 pages, 12 figure
Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies
Combining algebro-geometric methods and factorization techniques for finite
difference expressions we provide a complete and self-contained treatment of
all real-valued quasi-periodic finite-gap solutions of both the Toda and
Kac-van Moerbeke hierarchies. In order to obtain our principal new result, the
algebro-geometric finite-gap solutions of the Kac-van Moerbeke hierarchy, we
employ particular commutation methods in connection with Miura-type
transformations which enable us to transfer whole classes of solutions (such as
finite-gap solutions) from the Toda hierarchy to its modified counterpart, the
Kac-van Moerbeke hierarchy, and vice versa.Comment: LaTeX, to appear in Memoirs of the Amer. Math. So
Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
We describe the generalization of Wilson's Numerical Renormalization Group
method to quantum impurity models with a bosonic bath, providing a general
non-perturbative approach to bosonic impurity models which can access
exponentially small energies and temperatures. As an application, we consider
the spin-boson model, describing a two-level system coupled to a bosonic bath
with power-law spectral density, J(omega) ~ omega^s. We find clear evidence for
a line of continuous quantum phase transitions for subohmic bath exponents
0<s<1; the line terminates in the well-known Kosterlitz-Thouless transition at
s=1. Contact is made with results from perturbative renormalization group, and
various other applications are outlined.Comment: 4 pages, 5 figs, (v2) final version as publishe
The Complement System at the Embryo Implantation Site: Friend or Foe?
An inflammatory-like process and vascular remodeling represent the main changes that occur in decidua in the early phase of pregnancy. These changes are partly induced by trophoblast cells that colonize the decidua and are also contributed by the complement system, which can easily be activated as a result of tissue remodeling. Local control by several complement regulators including surface-bound and soluble molecules is critical to prevent complement-mediated tissue damage in normal pregnancy. C7 expressed on the endothelial cells (ECs) surface has been recognized as a novel complement regulator involved in the control of the proinflammatory effect of the terminal complement complex. The protective role of placental complement regulators in pregnancy is underscored by the recent finding of an association of preeclampsia with mutations in the genes encoding for some of these proteins. Complement components produced at feto-maternal interface serve an important function in placental development. C1q synthesized by decidual ECs and expressed on the cell surface is particularly important in this regard because it acts as a molecular bridge between endovascular trophoblast and ECs. C1q is also produced by extravillous trophoblast and is used to favor trophoblast migration through the decidua. Defective expression of C1q by trophoblast is associated with impaired trophoblast invasion of decidua and may have important implications in pregnancy disorders such as preeclampsia characterized by reduced vascular remodeling
Transport and Spectra in the Half-filled Hubbard Model: A Dynamical Mean Field Study
We study the issues of scaling and universality in spectral and transport
properties of the infinite dimensional particle--hole symmetric (half-filled)
Hubbard model within dynamical mean field theory. One of the simplest and
extensively used impurity solvers, namely the iterated perturbation theory
approach is reformulated to avoid problems such as analytic continuation of
Matsubara frequency quantities or calculating multi-dimensional integrals,
while taking full account of the very sharp structures in the Green's functions
that arise close to the Mott transitions and in the Mott insulator regime. We
demonstrate its viability for the half-filled Hubbard model. Previous known
results are reproduced within the present approach. The universal behavior of
the spectral functions in the Fermi liquid regime is emphasized, and adiabatic
continuity to the non-interacting limit is demonstrated. The dc resistivity in
the metallic regime is known to be a non-monotonic function of temperature with
a `coherence peak'. This feature is shown to be a universal feature occurring
at a temperature roughly equal to the low energy scale of the system. A
comparison to pressure dependent dc resistivity experiments on Selenium doped
NiS yields qualitatively good agreement. Resistivity hysteresis across the
Mott transition is shown to be described qualitatively within the present
framework. A direct comparison of the thermal hysteresis observed in VO
with our theoretical results yields a value of the hopping integral, which we
find to be in the range estimated through first-principle methods. Finally, a
systematic study of optical conductivity is carried out and the changes in
absorption as a result of varying interaction strength and temperature are
identified.Comment: 19 pages, 12 figure
Nonresonant inelastic light scattering in the Hubbard model
Inelastic light scattering from electrons is a symmetry-selective probe of
the charge dynamics within correlated materials. Many measurements have been
made on correlated insulators, and recent exact solutions in large dimensions
explain a number of anomalous features found in experiments. Here we focus on
the correlated metal, as described by the Hubbard model away from half filling.
We can determine the B1g Raman response and the inelastic X-ray scattering
along the Brillouin zone diagonal exactly in the large dimensional limit. We
find a number of interesting features in the light scattering response which
should be able to be seen in correlated metals such as the heavy fermions.Comment: 9 pages, 7 figures, typeset with ReVTe
Quantum Monte Carlo calculation of the finite temperature Mott-Hubbard transition
We present clear numerical evidence for the coexistence of metallic and
insulating dynamical mean field theory(DMFT) solutions in a half-filled
single-band Hubbard model with bare semicircular density of states at finite
temperatures. Quantum Monte Carlo(QMC) method is used to solve the DMFT
equations. We discuss important technical aspects of the DMFT-QMC which need to
be taken into account in order to obtain the reliable results near the
coexistence region. Among them are the critical slowing down of the iterative
solutions near phase boundaries, the convergence criteria for the DMFT
iterations, the interpolation of the discretized Green's function and the
reduction of QMC statistical and systematic errors. Comparison of our results
with those of other numerical methods is presented in a phase diagram.Comment: 4 pages, 5 figure
A Local Moment Approach to magnetic impurities in gapless Fermi systems
A local moment approach is developed for the single-particle excitations of a
symmetric Anderson impurity model (AIM), with a soft-gap hybridization
vanishing at the Fermi level with a power law r > 0. Local moments are
introduced explicitly from the outset, and a two-self-energy description is
employed in which the single-particle excitations are coupled dynamically to
low-energy transverse spin fluctuations. The resultant theory is applicable on
all energy scales, and captures both the spin-fluctuation regime of strong
coupling (large-U), as well as the weak coupling regime. While the primary
emphasis is on single particle dynamics, the quantum phase transition between
strong coupling (SC) and (LM) phases can also be addressed directly; for the
spin-fluctuation regime in particular a number of asymptotically exact results
are thereby obtained. Results for both single-particle spectra and SC/LM phase
boundaries are found to agree well with recent numerical renormalization group
(NRG) studies. A number of further testable predictions are made; in
particular, for r < 1/2, spectra characteristic of the SC state are predicted
to exhibit an r-dependent universal scaling form as the SC/LM phase boundary is
approached and the Kondo scale vanishes. Results for the `normal' r = 0 AIM are
moreover recovered smoothly from the limit r -> 0, where the resultant
description of single-particle dynamics includes recovery of Doniach-Sunjic
tails in the Kondo resonance, as well as characteristic low-energy Fermi liquid
behaviour.Comment: 52 pages, 19 figures, submitted to Journal of Physics: Condensed
Matte
Correlation and surface effects in Vanadium Oxides
Recent photoemission experiments have shown strong surface modifications in
the spectra from vanadium oxides as (V,Cr)_2O_3 or
(Sr,Ca)VO_3. The effective mass is enhanced at the surface and the coherent
part of the surface spectrum is narrowed as compared to the bulk. The
quasiparticle weight is more sensitive at the surface than in the bulk against
bandwidth variations. We investigate these effects theoretically considering
the single-band Hubbard model for a film geometry. A simplified dynamical
mean-field scheme is used to calculate the main features of the interacting
layer-dependent spectral function. It turns out that the experimentally
confirmed effects are inherent properties of a system of strongly correlated
electrons. The reduction of the weight and the variance of the coherent part of
the surface spectrum can be traced back to the reduced surface coordination
number. Surface correlation effects can be strongly amplified by changes of the
hopping integrals at the surface.Comment: to appear in PRB; 8 pages, 6 figure
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