High-Order Coupled Cluster Method Calculations for the Ground- and Excited-State Properties of the Spin-Half XXZ Model

In this article, we present new results of high-order coupled cluster method (CCM) calculations, based on a N\'eel model state with spins aligned in the $z$-direction, for both the ground- and excited-state properties of the spin-half {\it XXZ} model on the linear chain, the square lattice, and the simple cubic lattice. In particular, the high-order CCM formalism is extended to treat the excited states of lattice quantum spin systems for the first time. Completely new results for the excitation energy gap of the spin-half {\it XXZ} model for these lattices are thus determined. These high-order calculations are based on a localised approximation scheme called the LSUB$m$ scheme in which we retain all $k$-body correlations defined on all possible locales of $m$ adjacent lattice sites ($k \le m$). The ``raw'' CCM LSUB$m$ results are seen to provide very good results for the ground-state energy, sublattice magnetisation, and the value of the lowest-lying excitation energy for each of these systems. However, in order to obtain even better results, two types of extrapolation scheme of the LSUB$m$ results to the limit $m \to \infty$ (i.e., the exact solution in the thermodynamic limit) are presented. The extrapolated results provide extremely accurate results for the ground- and excited-state properties of these systems across a wide range of values of the anisotropy parameter.Comment: 31 Pages, 5 Figure

Low-energy parameters and spin gap of a frustrated spin-ss Heisenberg antiferromagnet with s≤32s \leq \frac{3}{2} on the honeycomb lattice

The coupled cluster method is implemented at high orders of approximation to investigate the zero-temperature $(T=0)$ phase diagram of the frustrated spin-$s$ $J_{1}$--$J_{2}$--$J_{3}$ antiferromagnet on the honeycomb lattice. The system has isotropic Heisenberg interactions of strength $J_{1}>0$, $J_{2}>0$ and $J_{3}>0$ between nearest-neighbour, next-nearest-neighbour and next-next-nearest-neighbour pairs of spins, respectively. We study it in the case $J_{3}=J_{2}\equiv \kappa J_{1}$, in the window $0 \leq \kappa \leq 1$ that contains the classical tricritical point (at $\kappa_{{\rm cl}}=\frac{1}{2}$) of maximal frustration, appropriate to the limiting value $s \to \infty$ of the spin quantum number. We present results for the magnetic order parameter $M$, the triplet spin gap $\Delta$, the spin stiffness $\rho_{s}$ and the zero-field transverse magnetic susceptibility $\chi$ for the two collinear quasiclassical antiferromagnetic (AFM) phases with N\'{e}el and striped order, respectively. Results for $M$ and $\Delta$ are given for the three cases $s=\frac{1}{2}$, $s=1$ and $s=\frac{3}{2}$, while those for $\rho_{s}$ and $\chi$ are given for the two cases $s=\frac{1}{2}$ and $s=1$. On the basis of all these results we find that the spin-$\frac{1}{2}$ and spin-1 models both have an intermediate paramagnetic phase, with no discernible magnetic long-range order, between the two AFM phases in their $T=0$ phase diagrams, while for $s > 1$ there is a direct transition between them. Accurate values are found for all of the associated quantum critical points. While the results also provide strong evidence for the intermediate phase being gapped for the case $s=\frac{1}{2}$, they are less conclusive for the case $s=1$. On balance however, at least the transition in the latter case at the striped phase boundary seems to be to a gapped intermediate state

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

Fifty Years of Candidate Pulsar Selection - What next?

For fifty years astronomers have been searching for pulsar signals in observational data. Throughout this time the process of choosing detections worthy of investigation, so called candidate selection, has been effective, yielding thousands of pulsar discoveries. Yet in recent years technological advances have permitted the proliferation of pulsar-like candidates, straining our candidate selection capabilities, and ultimately reducing selection accuracy. To overcome such problems, we now apply intelligent machine learning tools. Whilst these have achieved success, candidate volumes continue to increase, and our methods have to evolve to keep pace with the change. This talk considers how to meet this challenge as a community.Comment: 4 pages, submitted: Proceedings of Pulsar Astrophysics: The Next Fifty Years, IAU Symposium 33

Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method

We present a method for the direct calculation of the spin stiffness by means of the coupled cluster method. For the spin-half Heisenberg antiferromagnet on the square, the triangular and the cubic lattices we calculate the stiffness in high orders of approximation. For the square and the cubic lattices our results are in very good agreement with the best results available in the literature. For the triangular lattice our result is more precise than any other result obtained so far by other approximate method.Comment: 5 pages, 2 figure

Fabrication and optimization of a whiskerless Schottky barrier diode for submillimeter wave applications

The following accomplishments were made towards the goal of an optimized whiskerless diode chip for submillimeter wavelength applications. (1) Surface channel whiskerless diode structure was developed which offers excellent DC and RF characteristics, reduced shunt capacitance and simplified fabrication compared to mesa and proton isolated structures. (2) Reliable fabrication technology was developed for the surface channel structure. The new anode plating technology is a major improvement. (3) DC and RF characterization of the surface channel diode was compared with whisker contacted diodes. This data indicates electrical performance as good as the best reported for similar whisker contacted devices. (4) Additional batches of surface channel diodes were fabricated with excellent I-V and reduced shunt capacitance. (5) Large scale capacitance modelinng was done for the planar diode structure. This work revealed the importance of removing the substrate gallium arsenide for absolute minimum pad capacitance. (6) A surface channel diode was developed on quartz substrate and this substrate was completely removed after diode mounting for minimum parasitic capacitance. This work continues with the goal of producing excellent quality submillimeter wavelength planar diodes which satisfy the requirements of easy handling and robustness. These devices will allow the routine implementation of Schottky receivers into space-based applications at frequencies as high as 1 THz, and, in the future, beyond

Ab Initio Simulation of the Nodal Surfaces of Heisenberg Antiferromagnets

The spin-half Heisenberg antiferromagnet (HAF) on the square and triangular lattices is studied using the coupled cluster method (CCM) technique of quantum many-body theory. The phase relations between different expansion coefficients of the ground-state wave function in an Ising basis for the square lattice HAF is exactly known via the Marshall-Peierls sign rule, although no equivalent sign rule has yet been obtained for the triangular lattice HAF. Here the CCM is used to give accurate estimates for the Ising-expansion coefficients for these systems, and CCM results are noted to be fully consistent with the Marshall-Peierls sign rule for the square lattice case. For the triangular lattice HAF, a heuristic rule is presented which fits our CCM results for the Ising-expansion coefficients of states which correspond to two-body excitations with respect to the reference state. It is also seen that Ising-expansion coefficients which describe localised, $m$-body excitations with respect to the reference state are found to be highly converged, and from this result we infer that the nodal surface of the triangular lattice HAF is being accurately modeled. Using these results, we are able to make suggestions regarding possible extensions of existing quantum Monte Carlo simulations for the triangular lattice HAF.Comment: 24 pages, Latex, 3 postscript figure

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