Charge instabilities in strongly correlated bilayer systems

We investigate the charge-instabilities of the Hubbard-Holstein model with two coupled layers. In this system the scattering processes naturally separate into contributions which are either symmetric or antisymmetric combinations with respect to exchange of the layers. It turns out that the short-range strong correlations suppress finite wave-vector nesting instabilities for both symmetries but favor the occurrence of phase separation in the symmetric channel. Inclusion of a sizeable long-range Coulomb (LRC) interaction frustrates the q=0 instabilities and supports the formation of incommensurate charge-density waves (CDW). Upon reducing doping from half-filling and for small electron-phonon coupling g the CDW instability first occurs in the antisymmetric channel but both instability lines merge with increasing g. While LRC forces always suppress the phase separation instability in the symmetric channel, the CDW period in the antisymmetric sector tends to infinity (q_c -> 0) for sufficiently small Coulomb interaction. This feature allows for the possibility of singular scattering over the whole Fermi surface. We discuss possible implications of our results for the bilayer high-Tc cuprates.Comment: 14 pages, 8 figures, accepted for EPJ

Theory of isotope effect in photoemission spectra of high-T_c superconducting cuprates

We investigate the effect of isotope substitution on the electronic spectral functions within a model where the charge carriers are coupled to bosonic charge-order (CO) fluctuations centered around some mean frequency \omega_0 and with enhanced scattering at wave-vector q_c. It is shown that a mass dependence of \omega_0 is not sufficient in order to account, especially at high energies, for the dispersion shifts experimentally observed in an optimally doped superconducting cuprate. We argue that isotope substitution induces a change of the spatial CO correlations which gives good account of the experimental data.Comment: 5 pages and 2 figure

Performance of algebraic multigrid methods for non-symmetric matrices arising in particle methods

Large linear systems with sparse, non-symmetric matrices arise in the modeling of Markov chains or in the discretization of convection-diffusion problems. Due to their potential to solve sparse linear systems with an effort that is linear in the number of unknowns, algebraic multigrid (AMG) methods are of fundamental interest for such systems. For symmetric positive definite matrices, fundamental theoretical convergence results are established, and efficient AMG solvers have been developed. In contrast, for non-symmetric matrices, theoretical convergence results have been provided only recently. A property that is sufficient for convergence is that the matrix be an M-matrix. In this paper, we present how the simulation of incompressible fluid flows with particle methods leads to large linear systems with sparse, non-symmetric matrices. In each time step, the Poisson equation is approximated by meshfree finite differences. While traditional least squares approaches do not guarantee an M-matrix structure, an approach based on linear optimization yields optimally sparse M-matrices. For both types of discretization approaches, we investigate the performance of a classical AMG method, as well as an AMLI type method. While in the considered test problems, the M-matrix structure turns out not to be necessary for the convergence of AMG, problems can occur when it is violated. In addition, the matrices obtained by the linear optimization approach result in fast solution times due to their optimal sparsity.Comment: 16 pages, 7 figure

Fermi surface dichotomy on systems with fluctuating order

We investigate the effect of a dynamical collective mode coupled with quasiparticles at specific wavevectors only. This coupling describes the incipient tendency to order and produces shadow spectral features at high energies, while leaving essentially untouched the low energy quasiparticles. This allows to interpret seemingly contradictory experiments on underdoped cuprates, where many converging evidences indicate the presence of charge (stripe or checkerboard) order, which remains instead elusive in the Fermi surface obtained from angle-resolved photoemission experiments.Comment: 11 pages, 10 figure

Checkerboard and stripe inhomogeneities in cuprates

We systematically investigate charge-ordering phases by means of a restricted and unrestricted Gutzwiller approximation to the single-band Hubbard model with nearest ($t$) and next-nearest neighbor hopping ($t'$). When $|t'/t|$ is small, as appropriate for ${\rm La_{2-x}Sr_xCuO_4}$, stripes are found, whereas in compounds with larger $|t'/t|$ (such as ${\rm Ca_{2-x}Na_x CuO_2Cl_2}$ and ${\rm Bi_2Sr_2CaCu_2O_{8+\delta}}$) checkerboard structures are favored. In contrast to the linear doping dependence found for stripes the charge periodicity of checkerboard textures is locked to 4 unit cells over a wide doping range. In addition we find that checkerboard structures are favored at surfaces.Comment: 5 pages, 3 figure

Magnetic fluctuations from stripes in cuprates

Within the time-dependent Gutzwiller approximation for the Hubbard model we compute the magnetic fluctuations of vertical metallic stripes with parameters appropriate for La$_{1.875}$Ba$_{0.125}$CuO$_4$ (LBCO). For bond- and site-centered stripes the excitation spectra are similar, consisting of a low-energy incommensurate acoustic branch which merges into a ``resonance peak'' at the antiferromagnetic wave vector and several high-energy optical branches. The acoustic branch is similar to the result of theories assuming localized spins whereas the optical branches are significantly different. Results are in good agreement with a recent inelastic neutron study of LBCO.Comment: 4 pages, 2 eps figure

StaRMAP - A second order staggered grid method for spherical harmonics moment equations of radiative transfer

We present a simple method to solve spherical harmonics moment systems, such as the the time-dependent $P_N$ and $SP_N$ equations, of radiative transfer. The method, which works for arbitrary moment order $N$, makes use of the specific coupling between the moments in the $P_N$ equations. This coupling naturally induces staggered grids in space and time, which in turn give rise to a canonical, second-order accurate finite difference scheme. While the scheme does not possess TVD or realizability limiters, its simplicity allows for a very efficient implementation in Matlab. We present several test cases, some of which demonstrate that the code solves problems with ten million degrees of freedom in space, angle, and time within a few seconds. The code for the numerical scheme, called StaRMAP (Staggered grid Radiation Moment Approximation), along with files for all presented test cases, can be downloaded so that all results can be reproduced by the reader.Comment: 28 pages, 7 figures; StaRMAP code available at http://www.math.temple.edu/~seibold/research/starma