Entanglement perturbation theory for the elementary excitation in one dimension

The entanglement perturbation theory is developed to calculate the excitation spectrum in one dimension. Applied to the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model, it reproduces the des Cloiseaux-Pearson Bethe ansatz result. As for spin-1, the spin-triplet magnon spectrum has been determined for the first time for the entire Brillouin zone, including the Haldane gap at $k=\pi$

Dynamical Correlation Functions using the Density Matrix Renormalization Group

The density matrix renormalization group (DMRG) method allows for very precise calculations of ground state properties in low-dimensional strongly correlated systems. We investigate two methods to expand the DMRG to calculations of dynamical properties. In the Lanczos vector method the DMRG basis is optimized to represent Lanczos vectors, which are then used to calculate the spectra. This method is fast and relatively easy to implement, but the accuracy at higher frequencies is limited. Alternatively, one can optimize the basis to represent a correction vector for a particular frequency. The correction vectors can be used to calculate the dynamical correlation functions at these frequencies with high accuracy. By separately calculating correction vectors at different frequencies, the dynamical correlation functions can be interpolated and pieced together from these results. For systems with open boundaries we discuss how to construct operators for specific wavevectors using filter functions.Comment: minor revision, 10 pages, 15 figure

Density matrix algorithm for the calculation of dynamical properties of low dimensional systems

I extend the scope of the density matrix renormalization group technique developed by White to the calculation of dynamical correlation functions. As an application and performance evaluation I calculate the spin dynamics of the 1D Heisenberg chain.Comment: 4 pages + 4 figures in one Latex + 4 postscript file

Calculation of the singlet-triplet gap of the antiferromagnetic Heisenberg Model on the ladder

The ground state energy and the singlet-triplet energy gap of the antiferromagnetic Heisenberg model on a ladder is investigated using a mean field theory and the density matrix renormalization group. Spin wave theory shows that the corrections to the local magnetization are infinite. This indicates that no long range order occurs in this system. A flux-phase state is used to calculate the energy gap as a function of the transverse coupling, $J_\perp$, in the ladder. It is found that the gap is linear in $J_\perp$ for $J_\perp\gg 1$ and goes to zero for $J_\perp\to 0$. The mean field theory agrees well with the numerical results.Comment: 11pages,6 figures (upon request) Revtex 3.0, Report#CRPS-94-0

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

Second order quantum renormalisation group of XXZ chain with next nearest neighbour interactions

We have extended the application of quantum renormalisation group (QRG) to the anisotropic Heisenberg model with next-nearest neighbour (n-n-n) interaction. The second order correction has to be taken into account to get a self similar renormalized Hamiltonian in the presence of n-n-n-interaction. We have obtained the phase diagram of this model which consists of three different phases, i.e, spin-fluid, dimerised and Ne'el types which merge at the tri-critical point. The anisotropy of the n-n-n-term changes the phase diagram significantly. It has a dominant role in the Ne'el-dimer phase boundary. The staggered magnetisation as an order parameter defines the border between fluid-Ne'el and Ne'el-dimer phases. The improvement of the second order RG corrections on the ground state energy of the Heisenberg model is presented. Moreover, the application of second order QRG on the spin lattice model has been discussed generally. Our scheme shows that higher order corrections lead to an effective Hamiltonian with infinite range of interactions.Comment: 10 pages, 4 figures and 1 tabl

Models of turbulent dissipation regions in the diffuse interstellar medium

Supersonic turbulence is a large reservoir of suprathermal energy in the interstellar medium. Its dissipation, because it is intermittent in space and time, can deeply modify the chemistry of the gas. We further explore a hybrid method to compute the chemical and thermal evolution of a magnetized dissipative structure, under the energetic constraints provided by the observed properties of turbulence in the cold neutral medium. For the first time, we model a random line of sight by taking into account the relative duration of the bursts with respect to the thermal and chemical relaxation timescales of the gas. The key parameter is the turbulent rate of strain "a" due to the ambient turbulence. With the gas density, it controls the size of the dissipative structures, therefore the strength of the burst. For a large range of rates of strain and densities, the models of turbulent dissipation regions (TDR) reproduce the CH+ column densities observed in the diffuse medium and their correlation with highly excited H2. They do so without producing an excess of CH. As a natural consequence, they reproduce the abundance ratios of HCO+/OH and HCO+/H2O, and their dynamic range of about one order of magnitude observed in diffuse gas. Large C2H and CO abundances, also related to those of HCO+, are another outcome of the TDR models that compare well with observed values. The abundances and column densities computed for CN, HCN and HNC are one order of magnitude above PDR model predictions, although still significantly smaller than observed values

Ground-State Dynamical Correlation Functions: An Approach from Density Matrix Renormalization Group Method

A numerical approach to ground-state dynamical correlation functions from Density Matrix Renormalization Group (DMRG) is developed. Using sum rules, moments of a dynamic correlation function can be calculated with DMRG, and with the moments the dynamic correlation function can be obtained by the maximum entropy method. We apply this method to one-dimensional spinless fermion system, which can be converted to the spin 1/2 Heisenberg model in a special case. The dynamical density-density correlation function is obtained.Comment: 11 pages, latex, 4 figure

FUSE search for 10^5-10^6 K gas in the rich clusters of galaxies Abell 2029 and Abell 3112

Recent Chandra and XMM X-ray observations of rich clusters of galaxies have shown that the amount of hot gas which is cooling below ~1 keV is generally more modest than previous estimates. Yet, the real level of the cooling flows, if any, remains to be clarified by making observations sensitive to different temperature ranges. As a follow-up of the FUSE observations reporting a positive detection of the OVI doublet at 1032, 1038 Angstrom in the cluster of galaxies Abell 2597, which provided the first direct evidence for ~3x10^5 K gas in a cluster of galaxies, we have carried out sensitive spectroscopy of two rich clusters, Abell 2029 and Abell 3112 (z~0.07) located behind low HI columns. In neither of these clusters could we detect the OVI doublet, yielding fairly stringent limits of ~27 Msun yr-1 (Abell 2029) and ~25 Msun yr-1 (Abell 3112) to the cooling flow rates using the 10^5-10^6 K gas as a tracer. The non-detections support the emerging picture that the cooling-flow rates are much more modest than deduced from earlier X-ray observations.Comment: Astronomy & Astrophysics, in pres

Persistent Currents in the Heisenberg chain with a weak link

The Heisenberg chain with a weak link is studied, as a simple example of a quantum ring with a constriction or defect. The Heisenberg chain is equivalent to a spinless electron gas under a Jordan-Wigner transformation. Using density matrix renormalization group and quantum Monte Carlo methods we calculate the spin/charge stiffness of the model, which determines the strength of the `persistent currents'. The stiffness is found to scale to zero in the weak link case, in agreement with renormalization group arguments of Eggert and Affleck, and Kane and Fisher.Comment: 14 pages, 7 figures, 2 tables, no changes to paper, author list changed on archiv