Systematic Inclusion of High-Order Multi-Spin Correlations for the Spin-121\over2 XXZXXZ Models

We apply the microscopic coupled-cluster method (CCM) to the spin-$1\over2$ $XXZ$ models on both the one-dimensional chain and the two-dimensional square lattice. Based on a systematic approximation scheme of the CCM developed by us previously, we carry out high-order {\it ab initio} calculations using computer-algebraic techniques. The ground-state properties of the models are obtained with high accuracy as functions of the anisotropy parameter. Furthermore, our CCM analysis enables us to study their quantum critical behavior in a systematic and unbiased manner.Comment: (to appear in PRL). 4 pages, ReVTeX, two figures available upon request. UMIST Preprint MA-000-000

Phase Transitions in the Spin-Half J_1--J_2 Model

The coupled cluster method (CCM) is a well-known method of quantum many-body theory, and here we present an application of the CCM to the spin-half J_1--J_2 quantum spin model with nearest- and next-nearest-neighbour interactions on the linear chain and the square lattice. We present new results for ground-state expectation values of such quantities as the energy and the sublattice magnetisation. The presence of critical points in the solution of the CCM equations, which are associated with phase transitions in the real system, is investigated. Completely distinct from the investigation of the critical points, we also make a link between the expansion coefficients of the ground-state wave function in terms of an Ising basis and the CCM ket-state correlation coefficients. We are thus able to present evidence of the breakdown, at a given value of J_2/J_1, of the Marshall-Peierls sign rule which is known to be satisfied at the pure Heisenberg point (J_2 = 0) on any bipartite lattice. For the square lattice, our best estimates of the points at which the sign rule breaks down and at which the phase transition from the antiferromagnetic phase to the frustrated phase occurs are, respectively, given (to two decimal places) by J_2/J_1 = 0.26 and J_2/J_1 = 0.61.Comment: 28 pages, Latex, 2 postscript figure

Influence of quantum fluctuations on zero-temperature phase transitions between collinear and noncollinear states in frustrated spin systems

We study a square-lattice spin-half Heisenberg model where frustration is introduced by competing nearest-neighbor bonds of different signs. We discuss the influence of quantum fluctuations on the nature of the zero-temperature phase transitions from phases with collinear magnetic order at small frustration to phases with noncollinear spiral order at large frustration. We use the coupled cluster method (CCM) for high orders of approximation (up to LSUB6) and the exact diagonalization of finite systems (up to 32 sites) to calculate ground-state properties. The role of quantum fluctuations is examined by comparing the ferromagnetic-spiral and the antiferromagnetic-spiral transition within the same model. We find clear evidence that quantum fluctuations prefer collinear order and that they may favour a first order transition instead of a second order transition in case of no quantum fluctuations.Comment: 6 pages, 6 Postscipt figures; Accepted for publication in Phys. Rev.

Ab Initio Treatments of the Ising Model in a Transverse Field

In this article, new results are presented for the zero-temperature ground-state properties of the spin-half transverse Ising model on various lattices using three different approximate techniques. These are, respectively, the coupled cluster method, the correlated basis function method, and the variational quantum Monte Carlo method. The methods, at different levels of approximation, are used to study the ground-state properties of these systems, and the results are found to be in excellent agreement both with each other and with results of exact calculations for the linear chain and results of exact cumulant series expansions for lattices of higher spatial dimension. The different techniques used are compared and contrasted in the light of these results, and the constructions of the approximate ground-state wave functions are especially discussed.Comment: 28 Pages, 4 Figures, 1 Tabl

First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations

We prescribe a choice of 18 variables in all that casts the equations of the fully nonlinear characteristic formulation of general relativity in first--order quasi-linear canonical form. At the analytical level, a formulation of this type allows us to make concrete statements about existence of solutions. In addition, it offers concrete advantages for numerical applications as it now becomes possible to incorporate advanced numerical techniques for first order systems, which had thus far not been applicable to the characteristic problem of the Einstein equations, as well as in providing a framework for a unified treatment of the vacuum and matter problems. This is of relevance to the accurate simulation of gravitational waves emitted in astrophysical scenarios such as stellar core collapse.Comment: revtex4, 7 pages, text and references added, typos corrected, to appear in Phys. Rev.

Density matrix renormalisation group study of the correlation function of the bilinear-biquadratic spin-1 chain

Using the recently developed density matrix renormalization group approach, we study the correlation function of the spin-1 chain with quadratic and biquadratic interactions. This allows us to define and calculate the periodicity of the ground state which differs markedly from that in the classical analogue. Combining our results with other studies, we predict three phases in the region where the quadratic and biquadratic terms are both positive.Comment: 13 pages, Standard Latex File + 5 PostScript figures in separate (New version with SUBSTANTIAL REVISIONS to appear in J Phys A

High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States

In this article, we prove that exact representations of dimer and plaquette valence-bond ket ground states for quantum Heisenberg antiferromagnets may be formed via the usual coupled cluster method (CCM) from independent-spin product (e.g. N\'eel) model states. We show that we are able to provide good results for both the ground-state energy and the sublattice magnetization for dimer and plaquette valence-bond phases within the CCM. As a first example, we investigate the spin-half $J_1$--$J_2$ model for the linear chain, and we show that we are able to reproduce exactly the dimerized ground (ket) state at $J_2/J_1=0.5$. The dimerized phase is stable over a range of values for $J_2/J_1$ around 0.5. We present evidence of symmetry breaking by considering the ket- and bra-state correlation coefficients as a function of $J_2/J_1$. We then consider the Shastry-Sutherland model and demonstrate that the CCM can span the correct ground states in both the N\'eel and the dimerized phases. Finally, we consider a spin-half system with nearest-neighbor bonds for an underlying lattice corresponding to the magnetic material CaV$_4$O$_9$ (CAVO). We show that we are able to provide excellent results for the ground-state energy in each of the plaquette-ordered, N\'eel-ordered, and dimerized regimes of this model. The exact plaquette and dimer ground states are reproduced by the CCM ket state in their relevant limits.Comment: 34 pages, 13 figures, 2 table

Optimization of soliton ratchets in inhomogeneous sine-Gordon systems

Unidirectional motion of solitons can take place, although the applied force has zero average in time, when the spatial symmetry is broken by introducing a potential $V(x)$, which consists of periodically repeated cells with each cell containing an asymmetric array of strongly localized inhomogeneities at positions $x_{i}$. A collective coordinate approach shows that the positions, heights and widths of the inhomogeneities (in that order) are the crucial parameters so as to obtain an optimal effective potential $U_{opt}$ that yields a maximal average soliton velocity. $U_{opt}$ essentially exhibits two features: double peaks consisting of a positive and a negative peak, and long flat regions between the double peaks. Such a potential can be obtained by choosing inhomogeneities with opposite signs (e.g., microresistors and microshorts in the case of long Josephson junctions) that are positioned close to each other, while the distance between each peak pair is rather large. These results of the collective variables theory are confirmed by full simulations for the inhomogeneous sine-Gordon system

State-dependent Jastrow correlation functions for 4He nuclei

We calculate the ground-state energy for the nucleus 4He with V4 nucleon interactions, making use of a Jastrow description of the corresponding wavefunction with state-dependent correlation factors. The effect related to the state dependence of the correlation is quite important, lowering the upper bound for the ground-state energy by some 2 MeV.Comment: 10 pages, REVTeX, to be published in J. Phys. G: Nucl. Part. Phy

Global trends

Measuring trends in ozone, and most other geophysical variables, requires that a small systematic change with time be determined from signals that have large periodic and aperiodic variations. Their time scales range from the day-to-day changes due to atmospheric motions through seasonal and annual variations to 11 year cycles resulting from changes in the sun UV output. Because of the magnitude of all of these variations is not well known and highly variable, it is necessary to measure over more than one period of the variations to remove their effects. This means that at least 2 or more times the 11 year sunspot cycle. Thus, the first requirement is for a long term data record. The second related requirement is that the record be consistent. A third requirement is for reasonable global sampling, to ensure that the effects are representative of the entire Earth. The various observational methods relevant to trend detection are reviewed to characterize their quality and time and space coverage. Available data are then examined for long term trends or recent changes in ozone total content and vertical distribution, as well as related parameters such as stratospheric temperature, source gases and aerosols