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 d=1+ϵd=1+\epsilon dimensional half-filled Hubbard model

We study the low-energy asymptotics of the half-filled Hubbard model with a circular Fermi surface in $d=1+\epsilon$ continuous dimensions, based on the one-loop renormalization-group (RG) method. Peculiarity of the $d=1+\epsilon$ 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 $\epsilon>0$. 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 $U$ for $\epsilon>0$. 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