1,641 research outputs found
Luttinger liquids with boundaries: Power-laws and energy scales
We present a study of the one-particle spectral properties for a variety of
models of Luttinger liquids with open boundaries. We first consider the
Tomonaga-Luttinger model using bosonization. For weak interactions the boundary
exponent of the power-law suppression of the spectral weight close to the
chemical potential is dominated by a term linear in the interaction. This
motivates us to study the spectral properties also within the Hartree-Fock
approximation. It already gives power-law behavior and qualitative agreement
with the exact spectral function. For the lattice model of spinless fermions
and the Hubbard model we present numerically exact results obtained using the
density-matrix renormalization-group algorithm. We show that many aspects of
the behavior of the spectral function close to the boundary can again be
understood within the Hartree-Fock approximation. For the repulsive Hubbard
model with interaction U the spectral weight is enhanced in a large energy
range around the chemical potential. At smaller energies a power-law
suppression, as predicted by bosonization, sets in. We present an analytical
discussion of the crossover and show that for small U it occurs at energies
exponentially (in -1/U) close to the chemical potential, i.e. that bosonization
only holds on exponentially small energy scales. We show that such a crossover
can also be found in other models.Comment: 16 pages, 9 figures included, submitted for publicatio
The Gutzwiller wave function as a disentanglement prescription
The Gutzwiller variational wave function is shown to correspond to a
particular disentanglement of the thermal evolution operator, and to be
physically consistent only in the temperature range U<<kT<<E_F, the Fermi
energy of the non-interacting system. The correspondence is established without
using the Gutzwiller approximation. It provides a systematic procedure for
extending the ansatz to the strong-coupling regime. This is carried out to
infinite order in a dominant class of commutators. The calculation shows that
the classical idea of suppressing double occupation is replaced at low
temperatures by a quantum RVB-like condition, which involves phases at
neighboring sites. Low-energy phenomenologies are discussed in the light of
this result.Comment: Final version as accepted in EPJ B, 10 pages, no figure
From infinite to two dimensions through the functional renormalization group
We present a novel scheme for an unbiased and non-perturbative treatment of
strongly correlated fermions. The proposed approach combines two of the most
successful many-body methods, i.e., the dynamical mean field theory (DMFT) and
the functional renormalization group (fRG). Physically, this allows for a
systematic inclusion of non-local correlations via the flow equations of the
fRG, after the local correlations are taken into account non-perturbatively by
the DMFT. To demonstrate the feasibility of the approach, we present numerical
results for the two-dimensional Hubbard model at half-filling.Comment: 5 pages, 4 figure
Renormalization-group analysis of the one-dimensional extended Hubbard model with a single impurity
We analyze the one-dimensional extended Hubbard model with a single static
impurity by using a computational technique based on the functional
renormalization group. This extends previous work for spinless fermions to
spin-1/2 fermions. The underlying approximations are devised for weak
interactions and arbitrary impurity strengths, and have been checked by
comparing with density-matrix renormalization-group data. We present results
for the density of states, the density profile and the linear conductance.
Two-particle backscattering leads to striking effects, which are not captured
if the bulk system is approximated by its low-energy fixed point, the Luttinger
model. In particular, the expected decrease of spectral weight near the
impurity and of the conductance at low energy scales is often preceded by a
pronounced increase, and the asymptotic power laws are modified by logarithmic
corrections.Comment: 36 pages, 13 figures, revised version as publishe
Industrielle Innovationszyklen und sozial-ökologische Problemlagen:eine Sondierungsstudie zum Wandel von Nutzungskonkurrenzen und Umweltkonflikten unter Bedingungen der "Wissensgesellschaft"
Das Forschungsvorhaben stellt eine Sondierungsstudie zum Thema 'Industrielle Innovationszyklen und sozial-ökologische Problemlagen' dar, bei der im Rahmen einer Literaturanalyse der derzeitige Forschungsstand eruiert, seine Stärken und Schwächen analysiert und Empfehlungen für zukünftige Forschungsfragestellungen gegeben wurden. Zu den Stärken des bisherigen Forschungsstandes gehören die systematische Bezugsetzung von Innovationsfolgen zu den Zusammenhängen von Umwelt und Gesellschaft sowie die Möglichkeit der Einbeziehung der gesellschaftswissenschaftlichen Technik- und Risikoforschung in die Nachhaltigkeitsforschung. Zu den Schwächen des bisherigen Forschungsstandes gehören neben der unzureichenden Integration von Nutzungskonkurrenzen und Verteilungskonflikten in einen systematischen ökologisch-sozialwissenschaftlichen Ansatz vor allem die fehlende analytische Berücksichtigung eines sich abzeichnenden Übergangs zu einem neuen industriellen Innovationszyklus im Rahmen eines sozial-ökologischen Forschungsansatzes sowie das beträchtliche Defizit auf den Gebieten der Industrie- und Innovationsforschung. Zukünftiger Forschungsbedarf wird vor allem in den Bereichen eines Vergleichs der empirischen Verläufe und Folgen vergangener Innovationszyklen, einer Analyse gegenwärtiger Innovationswellen und einer generellen Analyse struktureller und dynamischer Muster sozial-ökologischer Transformationsprozesse gesehen.<br
Quantum phase transitions and collapse of the Mott gap in the dimensional half-filled Hubbard model
We study the low-energy asymptotics of the half-filled Hubbard model with a
circular Fermi surface in continuous dimensions, based on the
one-loop renormalization-group (RG) method. Peculiarity of the
dimensions is incorporated through the mathematica structure of the elementary
particle-partcile (PP) and particle-hole (PH) loops: infrared logarithmic
singularity of the PH loop is smeared for . The RG flows indicate
that a quantum phase transition (QPT) from a metallic phase to the Mott
insulator phase occurs at a finite on-site Coulomb repulsion for
. We also discuss effects of randomness.Comment: 12 pages, 10 eps figure
Exact analytic results for the Gutzwiller wave function with finite magnetization
We present analytic results for ground-state properties of Hubbard-type
models in terms of the Gutzwiller variational wave function with non-zero
values of the magnetization m. In dimension D=1 approximation-free evaluations
are made possible by appropriate canonical transformations and an analysis of
Umklapp processes. We calculate the double occupation and the momentum
distribution, as well as its discontinuity at the Fermi surface, for arbitrary
values of the interaction parameter g, density n, and magnetization m. These
quantities determine the expectation value of the one-dimensional Hubbard
Hamiltonian for any symmetric, monotonically increasing dispersion epsilon_k.
In particular for nearest-neighbor hopping and densities away from half filling
the Gutzwiller wave function is found to predict ferromagnetic behavior for
sufficiently large interaction U.Comment: REVTeX 4, 32 pages, 8 figure
Hole dynamics in generalized spin backgrounds in infinite dimensions
We calculate the dynamical behaviour of a hole in various spin backgrounds in
infinite dimensions, where it can be determined exactly. We consider hypercubic
lattices with two different types of spin backgrounds. On one hand we study an
ensemble of spin configurations with an arbitrary spin probability on each
sublattice. This model corresponds to a thermal average over all spin
configurations in the presence of staggered or uniform magnetic fields. On the
other hand we consider a definite spin state characterized by the angle between
the spins on different sublattices, i.e a classical spin system in an external
magnetic field. When spin fluctuations are considered, this model describes the
physics of unpaired particles in strong coupling superconductors.Comment: Accepted in Phys. Rev. B. 18 pages of text (1 fig. included) in Latex
+ 2 figures in uuencoded form containing the 2 postscripts (mailed
separately
Many-body position operator in lattice fermionic systems with periodic boundary conditions
A total position operator in the position representation is derived for
lattice fermionic systems with periodic boundary conditions. The operator is
shown to be Hermitian, the generator of translations in momentum space, and its
time derivative is shown to correspond to the total current operator in a
periodic system. The operator is such that its moments can be calculated up to
any order. To demonstrate its utility finite size scaling is applied to the
Brinkman-Rice transition as well as metallic and insulating Gutzwiller
wavefunctions.Comment: to appear in Journal of Physics A: Mathematical and General
(reference will be added later
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