New space research frequency band proposals in the 20- to 40.5-GHz range

Future space research communications systems may require spectra above 20 GHz. Frequency bands above 20 GHz are identified that are suitable for space research. The selection of the proper bands depends on consideration of interference with other radio services, adequate bandwidths, link performance, and technical requirements for practical implementation

Bogoliubov transformations and exact isolated solutions for simple non-adiabatic Hamiltonians

We present a new method for finding isolated exact solutions of a class of non-adiabatic Hamiltonians of relevance to quantum optics and allied areas. Central to our approach is the use of Bogoliubov transformations of the bosonic fields in the models. We demonstrate the simplicity and efficiency of this method by applying it to the Rabi Hamiltonian.Comment: LaTeX, 16 pages, 1 figure. Minor additions and journal re

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

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

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

Coupled Cluster Method Calculations Of Quantum Magnets With Spins Of General Spin Quantum Number

We present a new high-order coupled cluster method (CCM) formalism for the ground states of lattice quantum spin systems for general spin quantum number, $s$. This new ``general-$s$'' formalism is found to be highly suitable for a computational implementation, and the technical details of this implementation are given. To illustrate our new formalism we perform high-order CCM calculations for the one-dimensional spin-half and spin-one antiferromagnetic {\it XXZ} models and for the one-dimensional spin-half/spin-one ferrimagnetic {\it XXZ} model. The results for the ground-state properties of the isotropic points of these systems are seen to be in excellent quantitative agreement with exact results for the special case of the spin-half antiferromagnet and results of density matrix renormalisation group (DMRG) calculations for the other systems. Extrapolated CCM results for the sublattice magnetisation of the spin-half antiferromagnet closely follow the exact Bethe Ansatz solution, which contains an infinite-order phase transition at $\Delta=1$. By contrast, extrapolated CCM results for the sublattice magnetisation of the spin-one antiferromagnet using this same scheme are seen to go to zero at $\Delta \approx 1.2$, which is in excellent agreement with the value for the onset of the Haldane phase for this model. Results for sublattice magnetisations of the ferrimagnet for both the spin-half and spin-one spins are non-zero and finite across a wide range of $\Delta$, up to and including the Heisenberg point at $\Delta=1$.Comment: 5 Figures. J. Stat. Phys. 108, p. 401 (2002

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