12,863 research outputs found
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
-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 scheme in which we
retain all -body correlations defined on all possible locales of
adjacent lattice sites (). The ``raw'' CCM LSUB 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 results to the limit (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, -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,
. This new ``general-'' 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 . 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 , 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 , up to and including the Heisenberg point at
.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
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