Phase diagram of an exactly solvable t-J ladder model

We study a system of one-dimensional t-J models coupled to a ladder system. A special choice of the interaction between neighbouring rungs leads to an integrable model with supersymmetry, which is broken by the presence of rung interactions. We analyze the spectrum of low-lying excitations and ground state phase diagram at zero temperature.Comment: LaTeX, 8 pp. incl. 1 figur

Convergence of forecast distributions in a 100,000-member idealised convective-scale ensemble

Many operational weather services use ensembles of forecasts to generate probabilistic predictions. Computational costs generally limit the size of the ensemble to fewer than 100 members, although the large number of degrees of freedom in the forecast model would suggest that a vastly larger ensemble would be required to represent the forecast probability distribution accurately. In this study, we use a computationally efficient idealised model that replicates key properties of the dynamics and statistics of cumulus convection to identify how the sampling uncertainty of statistical quantities converges with ensemble size. Convergence is quantified by computing the width of the 95% confidence interval of the sampling distribution of random variables, using bootstrapping on the ensemble distributions at individual time and grid points. Using ensemble sizes of up to 100,000 members, it was found that for all computed distribution properties, including mean, variance, skew, kurtosis, and several quantiles, the sampling uncertainty scaled as n-1/2 for sufficiently large ensemble size n. This behaviour is expected from the Central Limit Theorem, which further predicts that the magnitude of the uncertainty depends on the distribution shape, with a large uncertainty for statistics that depend on rare events. This prediction was also confirmed, with the additional observation that such statistics also required larger ensemble sizes before entering the asymptotic regime. By considering two methods for evaluating asymptotic behaviour in small ensembles, we show that the large-n theory can be applied usefully for some forecast quantities even for the ensemble sizes in operational use today

Electronic Ladders with SO(5) Symmetry: Phase Diagrams and Correlations at half-filling

We construct a family of electronic ladder models with SO(5) symmetry which have exact ground states in the form of finitely correlated wave functions. Extensions for these models preserving this symmetry are studied using these states in a variational approach. Within this approach, the zero temperature phase diagram of these electronic ladders at half filling is obtained, reproducing the known results in the weak coupling (band insulator) and strong coupling regime, first studied by Scalapino, Zhang and Hanke. Finally, the compact form of the variational wave functions allows to compute various correlation functions for these systems.Comment: RevTeX+epsf macros, 23 pp. including figure

Elementary excitations in the gapped phase of a frustrated S=1/2 spin ladder: from spinons to the Haldane triplet

We use the variational matrix-product ansatz to study elementary excitations in the S=1/2 ladder with additional diagonal coupling, equivalent to a single S=1/2 chain with alternating exchange and next-nearest neighbor interaction. In absence of alternation the elementary excitation consists of two free S=1/2 particles ("spinons") which are solitons in the dimer order. When the nearest-neighbor exchange alternates, the "spinons" are confined into one S=1 excitation being a soliton in the generalized string order. Variational results are found to be in a qualitative agreement with the exact diagonalization data for 24 spins. We argue that such an approach gives a reasonably good description in a wide range of the model parameters.Comment: RevTeX, 13 pages, 11 embedded figures, uses psfig and multico

Thermodynamics of the (1,1/2) Ferrimagnet in Finite Magnetic Fields

We investigate the specific heat and magnetisation of a ferrimagnet with gS=1 and S=1/2 spins in a finite magnetic field using the transfer matrix DMRG down to T=0.025J. Ferromagnetic gapless and antiferromagnetic gapped excitations for H=0 lead to rich thermodynamics for H > 0. While the specific heat is characterized by a generic double peak structure, magnetisation reveals two critical fields, Hc1=1.76(1) and Hc2=3.00(1) with square-root behaviour in the T=0 magnetisation. Simple analytical arguments allow to understand these experimentally accessible findings.Comment: 5 pages, 7 eps figures, uses RevTeX, submitted to PR

Phase diagram and hidden order for generalized spin ladders

We investigate the phase diagram of antiferromagnetic spin ladders with additional exchange interactions on diagonal bonds by variational and numerical methods. These generalized spin ladders interpolate smoothly between the $S=1/2$ chain with competing nn and nnn interactions, the $S=1/2$ chain with alternating exchange and the antiferromagnetic $S=1$ chain. The Majumdar-Ghosh ground states are formulated as matrix product states and are shown to exhibit the same type of hidden order as the af $S=1$ chain. Generalized matrix product states are used for a variational calculation of the ground state energy and the spin and string correlation functions. Numerical (Lanczos) calculations of the energies of the ground state and of the low-lying excited states are performed, and compare reasonably with the variational approach. Our results support the hypothesis that the dimer and Majumdar-Ghosh points are in the same phase as the af $S=1$ chain.Comment: 23 pages, REVTEX, 7 figure

Models of impurities in valence bond spin chains and ladders

We present the class of models of a nonmagnetic impurity in S=1/2 generalized ladder with an AKLT-type valence bond ground state, and of a S=1/2 impurity in the S=1 AKLT chain. The ground state in presence of impurity can be found exactly. Recently studied phenomenon of local enhancement of antiferromagnetic correlations around the impurity is absent for this family of models.Comment: 4 pages revtex, 3 figures embedde

Elementary Excitations of Heisenberg Ferrimagnetic Spin Chains

We numerically investigate elementary excitations of the Heisenberg alternating-spin chains with two kinds of spins 1 and 1/2 antiferromagnetically coupled to each other. Employing a recently developed efficient Monte Carlo technique as well as an exact diagonalization method, we verify the spin-wave argument that the model exhibits two distinct excitations from the ground state which are gapless and gapped. The gapless branch shows a quadratic dispersion in the small-momentum region, which is of ferromagnetic type. With the intention of elucidating the physical mechanism of both excitations, we make a perturbation approach from the decoupled-dimer limit. The gapless branch is directly related to spin 1's, while the gapped branch originates from cooperation of the two kinds of spins.Comment: 7 pages, 7 Postscript figures, RevTe

Exact symmetry breaking ground states for quantum spin chains

We introduce a family of spin-1/2 quantum chains, and show that their exact ground states break the rotational and translational symmetries of the original Hamiltonian. We also show how one can use projection to construct a spin-3/2 quantum chain with nearest neighbor interaction, whose exact ground states break the rotational symmetry of the Hamiltonian. Correlation functions of both models are determined in closed form. Although we confine ourselves to examples, the method can easily be adapted to encompass more general models.Comment: 4 pages, RevTex. 4 figures, minor changes, new reference