Series Expansions for Excited States of Quantum Lattice Models

We show that by means of connected-graph expansions one can effectively generate exact high-order series expansions which are informative of low-lying excited states for quantum many-body systems defined on a lattice. In particular, the Fourier series coefficients of elementary excitation spectra are directly obtained. The numerical calculations involved are straightforward extensions of those which have already been used to calculate series expansions for ground-state correlations and $T=0$ susceptibilities in a wide variety of models. As a test, we have reproduced the known elementary excitation spectrum of the transverse-field Ising chain in its disordered phase.Comment: 9 pages, no figures, Revtex 3.0 The revised version corrects the incorrect (and unnecessary) statement in the original that H and H^eff are related by a unitary transformation; in fact they are related by via a similarity transformation. This has no implications for the calculations of spectra, but is important for matrix element

Spin-wave excitation spectra and spectral weights in square lattice antiferromagnets

Using a recently developed method for calculating series expansions of the excitation spectra of quantum lattice models, we obtain the spin-wave spectra for square lattice, $S=1/2$ Heisenberg-Ising antiferromagnets. The calculated spin-wave spectrum for the Heisenberg model is close to but noticeably different from a uniformly renormalized classical (large-$S$) spectrum with the renormalization for the spin-wave velocity of approximately $1.18$. The relative weights of the single-magnon and multi-magnon contributions to neutron scattering spectra are obtained for wavevectors throughout the Brillouin zone.Comment: Two postscript figures, 4 two-column page

Spin-S bilayer Heisenberg models: Mean-field arguments and numerical calculations

Spin-S bilayer Heisenberg models (nearest-neighbor square lattice antiferromagnets in each layer, with antiferromagnetic interlayer couplings) are treated using dimer mean-field theory for general S and high-order expansions about the dimer limit for S=1, 3/2,...,4. We suggest that the transition between the dimer phase at weak intraplane coupling and the Neel phase at strong intraplane coupling is continuous for all S, contrary to a recent suggestion based on Schwinger boson mean-field theory. We also present results for S=1 layers based on expansions about the Ising limit: In every respect the S=1 bilayers appear to behave like S=1/2 bilayers, further supporting our picture for the nature of the order-disorder phase transition.Comment: 6 pages, Revtex 3.0, 8 figures (not embedded in text

Simple Vortex States in Films of Type-I Ginzburg-Landau Superconductor

Sufficiently thin films of type-I superconductor in a perpendicular magnetic field exhibit a triangular vortex lattice, while thick films develop an intermediate state. To elucidate what happens between these two regimes, precise numerical calculations have been made within Ginzburg-Landau theory at $\kappa=0.5$ and 0.25 for a variety of vortex lattice structures with one flux quantum per unit cell. The phase diagram in the space of mean induction and film thickness includes a narrow wedge in which a square lattice is stable, surrounded by the domain of stability of the triangular lattice at thinner films/lower fields and, on the other side, rectangular lattices with continuously varying aspect ratio. The vortex lattice has an anomalously small shear modulus within and close to the square lattice phase.Comment: 21 pages, 6 figure

Phase Transitions in the Symmetric Kondo Lattice Model in Two and Three Dimensions

We present an application of high-order series expansion in the coupling constants for the ground state properties of correlated lattice fermion systems. Expansions have been generated up to order $(t/J)^{14}$ for $d=1$ and $(t/J)^8$ for $d=2,\ 3$ for certain properties of the symmetric Kondo lattice model. Analyzing the susceptibility series, we find evidence for a continuous phase transition from the ``spin liquid'' phase characteristic of a ``Kondo Insulator'' to an antiferromagnetically ordered phase in dimensions $d\ge2$ as the antiferromagnetic Kondo coupling is decreased. The critical point is estimated to be at $(t/J)_c\approx0.7$ for square lattice and $(t/J)_c\approx0.5$ for simple-cubic lattice.Comment: 12 pages, Revtex, replace previous corrupted fil

The role of microtubule movement in bidirectional organelle transport

We study the role of microtubule movement in bidirectional organelle transport in Drosophila S2 cells and show that EGFP-tagged peroxisomes in cells serve as sensitive probes of motor induced, noisy cytoskeletal motions. Multiple peroxisomes move in unison over large time windows and show correlations with microtubule tip positions, indicating rapid microtubule fluctuations in the longitudinal direction. We report the first high-resolution measurement of longitudinal microtubule fluctuations performed by tracing such pairs of co-moving peroxisomes. The resulting picture shows that motor-dependent longitudinal microtubule oscillations contribute significantly to cargo movement along microtubules. Thus, contrary to the conventional view, organelle transport cannot be described solely in terms of cargo movement along stationary microtubule tracks, but instead includes a strong contribution from the movement of the tracks.Comment: 24 pages, 5 figure

Perturbation Theory for Spin Ladders Using Angular-Momentum Coupled Bases

We compute bulk properties of Heisenberg spin-1/2 ladders using Rayleigh-Schr\"odinger perturbation theory in the rung and plaquette bases. We formulate a method to extract high-order perturbative coefficients in the bulk limit from solutions for relatively small finite clusters. For example, a perturbative calculation for an isotropic $2\times 12$ ladder yields an eleventh-order estimate of the ground-state energy per site that is within 0.02% of the density-matrix-renormalization-group (DMRG) value. Moreover, the method also enables a reliable estimate of the radius of convergence of the perturbative expansion. We find that for the rung basis the radius of convergence is $\lambda_c\simeq 0.8$, with $\lambda$ defining the ratio between the coupling along the chain relative to the coupling across the chain. In contrast, for the plaquette basis we estimate a radius of convergence of $\lambda_c\simeq 1.25$. Thus, we conclude that the plaquette basis offers the only currently available perturbative approach which can provide a reliable treatment of the physically interesting case of isotropic $(\lambda=1)$ spin ladders. We illustrate our methods by computing perturbative coefficients for the ground-state energy per site, the gap, and the one-magnon dispersion relation.Comment: 22 pages. 9 figure