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

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

One particle interchain hopping in coupled Hubbard chains

Interchain hopping in systems of coupled chains of correlated electrons is investigated by exact diagonalizations and Quantum-Monte-Carlo methods. For two weakly coupled Hubbard chains at commensurate densities (e.g. n=1/3) the splitting at the Fermi level between bonding and antibonding bands is strongly reduced (but not suppressed) by repulsive interactions extending to a few lattice spacings. The magnitude of this reduction is directly connected to the exponent $\alpha$ of the 1D Luttinger liquid. However, we show that the incoherent part of the single particle spectral function is much less affected by the interchain coupling. This suggests that incoherent interchain hopping could occur for intermediate $\alpha$ values.Comment: 4 pages, LaTeX 3.0, 7 PostScript figures in uuencoded for

A pulsed, mono-energetic and angular-selective UV photo-electron source for the commissioning of the KATRIN experiment

The KATRIN experiment aims to determine the neutrino mass scale with a sensitivity of 200 meV/c^2 (90% C.L.) by a precision measurement of the shape of the tritium $\beta$-spectrum in the endpoint region. The energy analysis of the decay electrons is achieved by a MAC-E filter spectrometer. To determine the transmission properties of the KATRIN main spectrometer, a mono-energetic and angular-selective electron source has been developed. In preparation for the second commissioning phase of the main spectrometer, a measurement phase was carried out at the KATRIN monitor spectrometer where the device was operated in a MAC-E filter setup for testing. The results of these measurements are compared with simulations using the particle-tracking software "Kassiopeia", which was developed in the KATRIN collaboration over recent years.Comment: 19 pages, 16 figures, submitted to European Physical Journal

Interrelation of Superconducting and Antiferromagnetic Gaps in High-Tc Compounds: a Test Case for a Microscopic Theory

Recent angle resolved photoemission (ARPES) data, which found evidence for a d-wave-like modulation of the antiferromagnetic gap, suggest an intimate interrelation between the antiferromagnetic insulator and the superconductor with its d-wave gap. This poses a new challenge to microscopic descriptions, which should account for this correlation between, at first sight, very different states of matter. Here, we propose a microscopic mechanism which provides a definite correlation between these two different gap structures: it is shown that a projected SO(5) theory, which aims at unifying antiferromagnetism and d-wave superconductivity via a common symmetry principle while explicitly taking the Mott-Hubbard gap into account, correctly describes the observed gap characteristics. Specifically, it accounts for both the dispersion and the order of magnitude difference between the antiferromagnetic gap modulation and the superconducting gap.Comment: 8 pages, 5 figure

Distribution of spectral weight in a system with disordered stripes

The ``band-structure'' of a disordered stripe array is computed and compared, at a qualitative level, to angle resolved photoemission experiments on the cuprate high temperature superconductors. The low-energy states are found to be strongly localized transverse to the stripe direction, so the electron dynamics is strictly one-dimensional (along the stripe). Despite this, aspects of the two dimensional band-structure Fermi surface are still vividly apparent.Comment: 10 pages, 11 figure