Cluster Perturbation Theory for Hubbard models

Cluster perturbation theory is a technique for calculating the spectral weight of Hubbard models of strongly correlated electrons, which combines exact diagonalizations on small clusters with strong-coupling perturbation theory at leading order. It is exact in both the strong- and weak-coupling limits and provides a good approximation to the spectral function at any wavevector. Following the paper by S\'en\'echal et al. (Phys. Rev. Lett. {\bf 84}, 522 (2000)), we provide a more complete description and derivation of the method. We illustrate some of its capabilities, in particular regarding the effect of doping, the calculation of ground state energy and double occupancy, the disappearance of the Fermi surface in the $t-t'$ Hubbard model, and so on. The method is applicable to any model with on-site repulsion only.Comment: 11 pages, 10 figures (RevTeX 4

Spectral functions for strongly correlated 5f-electrons

We calculate the spectral functions of model systems describing 5f-compounds adopting Cluster Perturbation Theory. The method allows for an accurate treatment of the short-range correlations. The calculated excitation spectra exhibit coherent 5f bands coexisting with features associated with local intra-atomic transitions. The findings provide a microscopic basis for partial localization. Results are presented for linear chains.Comment: 10 Page

Impact of water saturation on seismoelectric transfer functions: a laboratory study of coseismic phenomenon

Seismic waves propagating in a porous medium, under favourable conditions, generate measurable electromagnetic fields due to electrokinetic effects. It has been proposed, following experimental and numerical studies, that these so-called ‘seismoelectromagnetic' couplings depend on pore fluid properties. The theoretical frame describing these phenomena are based on the original Biot's theory, assuming that pores are fluid-filled. We study here the impact of a partially saturated medium on amplitudes of those seismoelectric couplings by comparing experimental data to an effective fluid model. We have built a 1-m-length-scale experiment designed for imbibition and drainage of an homogeneous silica sand; the experimental set-up includes a seismic source, accelerometers, electric dipoles and capacitance probes in order to monitor seismic and seismoelectric fields during water saturation. Apparent velocities and frequency spectra (in the kiloHertz range) are derived from seismic and electrical measurements during experiments in varying saturation conditions. Amplitudes of seismic and seismoelectric waves and their ratios (i.e. transfer functions) are discussed using a spectral analysis performed by continuous wavelet transform. The experiments reveal that amplitude ratios of seismic to coseismic electric signals remain rather constant as a function of the water saturation in the Sw=[0.2-0.9] range, consistently with theoretically predicted transfer function

Synthetic use of the primary kinetic isotope effect in hydrogen atom transfer: generation of α-aminoalkyl radicals.

addresses: School of Biosciences, University of Exeter, Geoffrey Pope Building, Stocker Road, Exeter, UKEX4 4QD. [email protected]: Journal Article; Research Support, Non-U.S. Gov'tCopyright © 2010 Royal Society of ChemistryThe extent to which deuterium can act as a protecting group to prevent unwanted 1,5-hydrogen atom transfer to aryl and vinyl radical intermediates was examined in the context of the generation of α-aminoalkyl radicals in a pyrrolidine ring. Intra- and intermolecular radical trapping following hydrogen atom transfer provides an illustration of the use of the primary kinetic isotope effect in directing the outcome of synthetic C-C bond-forming processes

The spectral weight of the Hubbard model through cluster perturbation theory

We calculate the spectral weight of the one- and two-dimensional Hubbard models, by performing exact diagonalizations of finite clusters and treating inter-cluster hopping with perturbation theory. Even with relatively modest clusters (e.g. 12 sites), the spectra thus obtained give an accurate description of the exact results. Thus, spin-charge separation (i.e. an extended spectral weight bounded by singularities) is clearly recognized in the one-dimensional Hubbard model, and so is extended spectral weight in the two-dimensional Hubbard model.Comment: 4 pages, 5 figure

Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model

The ground states of the two-dimensional repulsive Hubbard model are studied within the unrestricted Hartree-Fock (UHF) theory. Magnetic and charge properties are determined by systematic, large-scale, exact numerical calculations, and quantified as a function of electron doping $h$. In the solution of the self-consistent UHF equations, multiple initial configurations and simulated annealing are used to facilitate convergence to the global minimum. New approaches are employed to minimize finite-size effects in order to reach the thermodynamic limit. At low to moderate interacting strengths and low doping, the UHF ground state is a linear spin-density wave (l-SDW), with antiferromagnetic order and a modulating wave. The wavelength of the modulating wave is $2/h$. Corresponding charge order exists but is substantially weaker than the spin order, hence holes are mobile. As the interaction is increased, the l-SDW states evolves into several different phases, with the holes eventually becoming localized. A simple pairing model is presented with analytic calculations for low interaction strength and small doping, to help understand the numerical results and provide a physical picture for the properties of the SDW ground state. By comparison with recent many-body calculations, it is shown that, for intermediate interactions, the UHF solution provides a good description of the magnetic correlations in the true ground state of the Hubbard model.Comment: 13 pages, 17 figure, 0 table

Neighbor Detection Induces Organ-Specific Transcriptomes, Revealing Patterns Underlying Hypocotyl-Specific Growth.

In response to neighbor proximity, plants increase the growth of specific organs (e.g., hypocotyls) to enhance access to sunlight. Shade enhances the activity of Phytochrome Interacting Factors (PIFs) by releasing these bHLH transcription factors from phytochrome B-mediated inhibition. PIFs promote elongation by inducing auxin production in cotyledons. In order to elucidate spatiotemporal aspects of the neighbor proximity response, we separately analyzed gene expression patterns in the major light-sensing organ (cotyledons) and in rapidly elongating hypocotyls of Arabidopsis thaliana PIFs initiate transcriptional reprogramming in both organs within 15 min, comprising regulated expression of several early auxin response genes. This suggests that hypocotyl growth is elicited by both local and distal auxin signals. We show that cotyledon-derived auxin is both necessary and sufficient to initiate hypocotyl growth, but we also provide evidence for the functional importance of the local PIF-induced response. With time, the transcriptional response diverges increasingly between organs. We identify genes whose differential expression may underlie organ-specific elongation. Finally, we uncover a growth promotion gene expression signature shared between different developmentally regulated growth processes and responses to the environment in different organs

The Fermi Liquid as a Renormalization Group Fixed Point: the Role of Interference in the Landau Channel

We apply the finite-temperature renormalization-group (RG) to a model based on an effective action with a short-range repulsive interaction and a rotation invariant Fermi surface. The basic quantities of Fermi liquid theory, the Landau function and the scattering vertex, are calculated as fixed points of the RG flow in terms of the effective action's interaction function. The classic derivations of Fermi liquid theory, which apply the Bethe-Salpeter equation and amount to summing direct particle-hole ladder diagrams, neglect the zero-angle singularity in the exchange particle-hole loop. As a consequence, the antisymmetry of the forward scattering vertex is not guaranteed and the amplitude sum rule must be imposed by hand on the components of the Landau function. We show that the strong interference of the direct and exchange processes of particle-hole scattering near zero angle invalidates the ladder approximation in this region, resulting in temperature-dependent narrow-angle anomalies in the Landau function and scattering vertex. In this RG approach the Pauli principle is automatically satisfied. The consequences of the RG corrections on Fermi liquid theory are discussed. In particular, we show that the amplitude sum rule is not valid.Comment: 25 pages, RevTeX 3.