A note on density correlations in the half-filled Hubbard model

We consider density-density correlations in the one-dimensional Hubbard model at half filling. On intuitive grounds one might expect them to exhibit an exponential decay. However, as has been noted recently, this is not obvious from the Bethe Ansatz/conformal field theory (BA/CFT) approach. We show that by supplementing the BA/CFT analysis with simple symmetry arguments one can easily prove that correlations of the lattice density operators decay exponentially.Comment: 3 pages, RevTe

A possible heterozygous advantage in muscular dystrophy

In certain autosomal recessive disorders there is suggestive evidence that heterozygous carriers may have some selective advantage over normal homozygotes. These include, for example, cystic fibrosis, Tay-Sachs disease and phenylketonuria. The best example so far, however, is that of significant heterozygous advantage in sickle-cell anaemia with increased resistance to falciparum malaria. 

Effects of Umklapp Scattering on Electronic States in One Dimension

The effects of Umklapp scattering on electronic states are studied in one spatial dimension at absolute zero. The model is basically the Hubbard model, where parameters characterizing the normal ($U$) and Umklapp ($V$) scattering are treated independently. The density of states is calculated in the t-matrix approximation by taking only the forward and Umklapp scattering into account. It is found that the Umklapp scattering causes the global splitting of the density of states. In the presence of sufficiently strong Umklapp scattering, a pole in the t-matrix appears in the upper half plane, signalling an instability towards the '$G/2-$pairing' ordered state ($G$ is the reciprocal lattice vector), whose consequences are studied in the mean field approximation. It turns out that this ordered state coexists with spin-density-wave state and also brings about Cooper-pairs. A phase diagram is determined in the plane of $V$ and electron filling $n$.Comment: 22 pages, LaTeX, 17 figures included, uses jpsj.st

Phase separation and pairing in coupled chains and planes

A generalization of the $t-J$ model in a system of two coupled chains or planes is studied by numerical diagonalization of small clusters. In particular, the effect of density fluctuations between these one- or two-dimensional coupled layerson intralayer phase separation and pairing is analyzed. The most robust signals of superconductivity are found at quarter filling for couplings just before the fully interlayer phase separated regime. The possibility of an enhancement of the intralayer superconducting pairing correlations by the interlayer couplings is investigated.Comment: 13 pages + 3 figures, available upon request, LATEX, preprint ORNL/CCIP/93/1

Static versus dynamic fluctuations in the one-dimensional extended Hubbard model

The extended Hubbard Hamiltonian is a widely accepted model for uncovering the effects of strong correlations on the phase diagram of low-dimensional systems, and a variety of theoretical techniques have been applied to it. In this paper the world-line quantum Monte Carlo method is used to study spin, charge, and bond order correlations of the one-dimensional extended Hubbard model in the presence of coupling to the lattice. A static alternating lattice distortion (the ionic Hubbard model) leads to enhanced charge density wave correlations at the expense of antiferromagnetic order. When the lattice degrees of freedom are dynamic (the Hubbard-Holstein model), we show that a similar effect occurs even though the charge asymmetry must arise spontaneously. Although the evolution of the total energy with lattice coupling is smooth, the individual components exhibit sharp crossovers at the phase boundaries. Finally, we observe a tendency for bond order in the region between the charge and spin density wave phases.Comment: Corrected typos. (10 pages, 9 figures

Luther-Emery Stripes, RVB Spin Liquid Background and High Tc Superconductivity

The stripe phase in high Tc cuprates is modeled as a single stripe coupled to the RVB spin liquid background by the single particle hopping process. In normal state, the strong pairing correlation inherent in RVB state is thus transfered into the Luttinger stripe and drives it toward spin-gap formation described by Luther-Emery Model. The establishment of global phase coherence in superconducting state contributes to a more relevant coupling to Luther-Emery Stripe and leads to gap opening in both spin and charge sectors. Physical consequences of the present picture are discussed, and emphasis is put on the unification of different energy scales relevant to cuprates, and good agreement is found with the available experimental results, especially in ARPES.Comment: 4 pages, RevTe

Classical Phase Fluctuations in High Temperature Superconductors

Phase fluctuations of the superconducting order parameter play a larger role in the cuprates than in conventional BCS superconductors because of the low superfluid density of a doped insulator. In this paper, we analyze an XY model of classical phase fluctuations in the high temperature superconductors using a low-temperature expansion and Monte Carlo simulations. In agreement with experiment, the value of the superfluid density at temperature T=0 is a quite robust predictor of Tc, and the evolution of the superfluid density with T, including its T-linear behavior at low temperature, is insensitive to microscopic details.Comment: 4 pages, 1 figur

Superconductivity of a Metallic Stripe Embedded in an Antiferromagnet

We study a simple model for the metallic stripes found in $La_{1.6-x}Nd_{0.4}Sr_xCuO_4$: two chain Hubbard ladder embedded in a static antiferromagnetic environments. We consider two cases: a ``topological stripe'', for which the phase of the Neel order parameter shifts by $\pi$ across the ladder, and a ``non-topological stripe'', for which there is no phase shift across the ladder. We perform one-loop renormalization group calculations to determine the low energy properties. We compare the results with those of the isolated ladder and show that for small doping superconductivity is enhanced in the topological stripe, and suppressed in the non-topological one. In the topological stripe, the superconducting order parameter is a mixture of a spin singlet component with zero momentum and a spin triplet component with momentum $\pi$. We argue that this mixture is generic, and is due to the presence of a new term in the quantum Ginzburg-Landau action. Some consequences of this mixing are discussed.Comment: 6 pages, 3 eps figure

Optical sum in Nearly Antiferromagnetic Fermi Liquid Model

We calculate the optical sum (OS) and the kinetic energy (KE) for a tight binding band in the Nearly Antiferromagnetic Fermi Liquid (NAFFL) model which has had some success in describing the electronic structure of the high $T_c$ cuprates. The interactions among electrons due to the exchange of spin fluctuations profoundly change the probability of occupation $(n_{{\bf k},\sigma})$ of states of momentum {\bf k} and spin $\sigma$ which is the central quantity in the calculations of OS and KE. Normal and superconducting states are considered as a function of temperature. Both integrals are found to depend importantly on interactions and an independent electron model is inadequate.Comment: 9 Pages, 5 Figures Accepted for publication in Phys. Rev.