Charge order induced by electron-lattice interaction in NaV2O5

We present Density Matrix Renormalization Group calculations of the ground-state properties of quarter-filled ladders including static electron-lattice coupling. Isolated ladders and two coupled ladders are considered, with model parameters obtained from band-structure calculations for $\alpha^\prime$-NaV$_2$O$_5$. The relevant Holstein coupling to the lattice causes static out-of-plane lattice distortions, which appear concurrently with a charge-ordered state and which exhibit the same zigzag pattern observed in experiments. The inclusion of electron-lattice coupling drastically reduces the critical nearest-neighbor Coulomb repulsion $V_c$ needed to obtain the charge-ordered state. No spin gap is present in the ordered phase. The charge ordering is driven by the Coulomb repulsion and the electron-lattice interaction. With electron-lattice interaction, coupling two ladders has virtually no effect on $V_c$ or on the characteristics of the charge-ordered phase. At V=0.46\eV, a value consistent with previous estimates, the lattice distortion, charge gap, charge order parameter, and the effective spin coupling are in good agreement with experimental data for NaV$_2$O_5$.Comment: 7 pages, 9 figure

Persistent current of two-chain Hubbard model with impurities

The interplay between impurities and interactions is studied in the gapless phase of two-chain Hubbard model in order to see how the screening of impurity potentials due to repulsive interactions in single-chain model will be changed by increasing the number of channels. Renormalization group calculations show that charge stiffness, and hence persistent current, of the two-chain model are less enhanced by interactions than single chain case.Comment: 4 Pages, RevTeX, No figures, Submitted to PR

Conductivity of Doped Two-Leg Ladders

Recently, conductivity measurements were performed on the hole-doped two-leg ladder material Sr_{14-x}Ca_xCu_{24}O_{41}. In this work, we calculate the conductivity for doped two-leg ladders using a model of hole-pairs forming a strongly correlated liquid - a single component Luttinger liquid - in the presence of disorder. Quantum interference effects are handled using renormalization group methods. We find that our model can account for the low energy features of the experimental results. However, at higher energies the experiments show deviations from the predictions of this model. Using the results of our calculations as well as results on the ground state of doped two-leg ladders, we suggest a scenario to account for the higher energy features of the experimental results.Comment: 5 pages, 3 postscript figure

Modularity clustering is force-directed layout

Two natural and widely used representations for the community structure of networks are clusterings, which partition the vertex set into disjoint subsets, and layouts, which assign the vertices to positions in a metric space. This paper unifies prominent characterizations of layout quality and clustering quality, by showing that energy models of pairwise attraction and repulsion subsume Newman and Girvan's modularity measure. Layouts with optimal energy are relaxations of, and are thus consistent with, clusterings with optimal modularity, which is of practical relevance because both representations are complementary and often used together.Comment: 9 pages, 7 figures, see http://code.google.com/p/linloglayout/ for downloading the graph clustering and layout softwar

Charge-order transition in the extended Hubbard model on a two-leg ladder

We investigate the charge-order transition at zero temperature in a two-leg Hubbard ladder with additional nearest-neighbor Coulomb repulsion V using the Density Matrix Renormalization Group technique. We consider electron densities between quarter and half filling. For quarter filling and U=8t, we find evidence for a continuous phase transition between a homogeneous state at small V and a broken-symmetry state with "checkerboard" [wavevector Q=(pi,pi)] charge order at large V. This transition to a checkerboard charge-ordered state remains present at all larger fillings, but becomes discontinuous at sufficiently large filling. We discuss the influence of U/t on the transition and estimate the position of the tricritical points.Comment: 4 pages, 5 figs, minor changes, accepted for publication in PRB R