Density matrix renormalisation group for a quantum spin chain at non-zero temperature

We apply a recent adaptation of White's density matrix renormalisation group (DMRG) method to a simple quantum spin model, the dimerised $XY$ chain, in order to assess the applicabilty of the DMRG to quantum systems at non-zero temperature. We find that very reasonable results can be obtained for the thermodynamic functions down to low temperatures using a very small basis set. Low temperature results are found to be most accurate in the case when there is a substantial energy gap.Comment: 6 pages, Standard Latex File + 7 PostScript figures available on reques

Small-Angle X-ray and neutron scattering from diamond single crystals

Results of Small-Angle Scattering study of diamonds with various types of point and extended defects and different degrees of annealing are presented. It is shown that thermal annealing and/or mechanical deformation cause formation of nanosized planar and threedimensional defects giving rise to Small-Angle Scattering. The defects are often facetted by crystallographic planes 111, 100, 110, 311, 211 common for diamond. The scattering defects likely consist of clusters of intrinsic and impurity-related defects; boundaries of mechanical twins also contribute to the SAS signal. There is no clear correlation between concentration of nitrogen impurity and intensity of the scattering.Comment: 6 pages, 5 figures; presented at SANS-YuMO User Meeting 2011, Dubna, Russi

Nanoscale piezoelectric response across a single antiparallel ferroelectric domain wall

Surprising asymmetry in the local electromechanical response across a single antiparallel ferroelectric domain wall is reported. Piezoelectric force microscopy is used to investigate both the in-plane and out-of- plane electromechanical signals around domain walls in congruent and near-stoichiometric lithium niobate. The observed asymmetry is shown to have a strong correlation to crystal stoichiometry, suggesting defect-domain wall interactions. A defect-dipole model is proposed. Finite element method is used to simulate the electromechanical processes at the wall and reconstruct the images. For the near-stoichiometric composition, good agreement is found in both form and magnitude. Some discrepancy remains between the experimental and modeling widths of the imaged effects across a wall. This is analyzed from the perspective of possible electrostatic contributions to the imaging process, as well as local changes in the material properties in the vicinity of the wall

A density matrix renormalisation group algorithm for quantum lattice systems with a large number of states per site

A variant of White's density matrix renormalisation group scheme which is designed to compute low-lying energies of one-dimensional quantum lattice models with a large number of degrees of freedom per site is described. The method is tested on two exactly solvable models---the spin-1/2 antiferromagnetic Heisenberg chain and a dimerised XY spin chain. To illustrate the potential of the method, it is applied to a model of spins interacting with quantum phonons. It is shown that the method accurately resolves a number of energy gaps on periodic rings which are sufficiently large to afford an accurate investigation of critical properties via the use of finite-size scaling theory.Comment: RevTeX, 8 pages, 2 figure

An output-sensitive algorithm for the minimization of 2-dimensional String Covers

String covers are a powerful tool for analyzing the quasi-periodicity of 1-dimensional data and find applications in automata theory, computational biology, coding and the analysis of transactional data. A \emph{cover} of a string $T$ is a string $C$ for which every letter of $T$ lies within some occurrence of $C$. String covers have been generalized in many ways, leading to \emph{k-covers}, \emph{$\lambda$-covers}, \emph{approximate covers} and were studied in different contexts such as \emph{indeterminate strings}. In this paper we generalize string covers to the context of 2-dimensional data, such as images. We show how they can be used for the extraction of textures from images and identification of primitive cells in lattice data. This has interesting applications in image compression, procedural terrain generation and crystallography

Evaluation of synthetic vascular grafts in a mouse carotid grafting model

Current animal models for the evaluation of synthetic grafts are lacking many of the molecular tools and transgenic studies available to other branches of biology. A mouse model of vascular grafting would allow for the study of molecular mechanisms of graft failure, including in the context of clinically relevant disease states. In this study, we comprehensively characterise a sutureless grafting model which facilitates the evaluation of synthetic grafts in the mouse carotid artery. Using conduits electrospun from polycaprolactone (PCL) we show the gradual development of a significant neointima within 28 days, found to be greatest at the anastomoses. Histological analysis showed temporal increases in smooth muscle cell and collagen content within the neointima, demonstrating its maturation. Endothelialisation of the PCL grafts, assessed by scanning electron microscopy (SEM) analysis and CD31 staining, was near complete within 28 days, together replicating two critical aspects of graft performance. To further demonstrate the potential of this mouse model, we used longitudinal non-invasive tracking of bone-marrow mononuclear cells from a transgenic mouse strain with a dual reporter construct encoding both luciferase and green fluorescent protein (GFP). This enabled characterisation of mononuclear cell homing and engraftment to PCL using bioluminescence imaging and histological staining over time (7, 14 and 28 days). We observed peak luminescence at 7 days post-graft implantation that persisted until sacrifice at 28 days. Collectively, we have established and characterised a high-throughput model of grafting that allows for the evaluation of key clinical drivers of graft performance.Alex H.P. Chan, Richard P. Tan, Praveesuda L. Michael, Bob S.L. Lee, Laura Z. Vanags, Martin K.C. Ng, Christina A. Bursill, Steven G. Wis

A numerical method for detecting incommensurate correlations in the Heisenberg zigzag ladder

We study two Heisenberg spin-1/2 chains coupled by a frustrating ``zigzag'' interaction. We are particularly interested in the regime of weak interchain coupling, which is difficult to analyse by either numerical or analytical methods. Previous density matrix renormalisation group (DMRG) studies of the isotropic model with open boundary conditions and sizeable interchain coupling have established the presence of incommensurate correlations and of a spectral gap. By using twisted boundary conditions with arbitrary twist angle, we are able to determine the incommensurabilities both in the isotropic case and in the presence of an exchange anisotropy by means of exact diagonalisation of relatively short finite chains of up to 24 sites. Using twisted boundary conditions results in a very smooth dependence of the incommensurabilities on system size, which makes the extrapolation to infinite systems significantly easier than for open or periodic chains.Comment: 6 pages, including 7 figure

Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain

The density matrix renormalization group (``DMRG'') discovered by White has shown to be a powerful method to understand the properties of many one dimensional quantum systems. In the case where renormalization eventually converges to a fixed point we show that quantum states in the thermodynamic limit with periodic boundary conditions can be simply represented by a special type of product ground state with a natural description of Bloch states of elementary excitations that are spin-1 solitons. We then observe that these states can be rederived through a simple variational ansatz making no reference to a renormalization construction. The method is tested on the spin-1 Heisenberg model.Comment: 13 pages uuencoded compressed postscript including figure

The strength of frustration and quantum fluctuations in LiVCuO4

For the 1D-frustrated ferromagnetic J_1-J_2 model with interchain coupling added, we analyze the dynamical and static structure factor S(k,omega), the pitch angle phi of the magnetic structure, the magnetization curve of edge-shared chain cuprates, and focus on LiCuVO4 for which neither a perturbed spinon nor a spin wave approach can be applied. phi is found to be most sensitive to the interplay of frustration and quantum fluctuations. For LiVCuO4 the obtained exchange parameters J are in accord with the results for a realistic 5-band extended Hubbard model and LSDA + U predictions yielding alpha=J_2/|J_1| about 0.75 in contrast to 5.5 > alpha > 1.42 suggested in the literature. The alpha-regime of the empirical phi-values in NaCu2O2 and linarite are considered, too.Comment: 7 pages, 7 figures, (1 figure added), improved text including also the abstract (the present second version has been submitted to EPL 26.10.2011, so far with one missing first referee report

Phase diagram of a Heisenberg spin-Peierls model with quantum phonons

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a non-zero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, which the model maps to in the anti-adiabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.Comment: RevTeX, 5 pages, 3 eps figures included using epsf. Improved theories in adiabatic and non-adiabatic regimes give better agreement with DMRG. This version accepted in Physical Review Letter