144 research outputs found
Quantum Phase Transitions and the Extended Coupled Cluster Method
We discuss the application of an extended version of the coupled cluster
method to systems exhibiting a quantum phase transition. We use the lattice
O(4) non-linear sigma model in (1+1)- and (3+1)-dimensions as an example. We
show how simple predictions get modified, leading to the absence of a phase
transition in (1+1) dimensions, and strong indications for a phase transition
in (3+1) dimensions
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
Single-Particle Green Functions in Exactly Solvable Models of Bose and Fermi Liquids
Based on a class of exactly solvable models of interacting bose and fermi
liquids, we compute the single-particle propagators of these systems exactly
for all wavelengths and energies and in any number of spatial dimensions. The
field operators are expressed in terms of bose fields that correspond to
displacements of the condensate in the bose case and displacements of the fermi
sea in the fermi case.
Unlike some of the previous attempts, the present attempt reduces the answer
for the spectral function in any dimension in both fermi and bose systems to
quadratures.
It is shown that when only the lowest order sea-displacement terms are
included, the random phase approximation in its many guises is recovered in the
fermi case, and Bogoliubov's theory in the bose case. The momentum distribution
is evaluated using two different approaches, exact diagonalisation and the
equation of motion approach.
The novelty being of course, the exact computation of single-particle
properties including short wavelength behaviour.Comment: Latest version to be published in Phys. Rev. B. enlarged to around 40
page
Time evolution of the Rabi Hamiltonian from the unexcited vacuum
The Rabi Hamiltonian describes a single mode of electromagnetic radiation
interacting with a two-level atom. Using the coupled cluster method, we
investigate the time evolution of this system from an initially empty field
mode and an unexcited atom. We give results for the atomic inversion and field
occupation, and find that the virtual processes cause the field to be squeezed.
No anti-bunching occurs.Comment: 25 pages, 8 figures, RevTe
An extension of the coupled-cluster method: A variational formalism
A general quantum many-body theory in configuration space is developed by
extending the traditional coupled cluter method (CCM) to a variational
formalism. Two independent sets of distribution functions are introduced to
evaluate the Hamiltonian expectation. An algebraic technique for calculating
these distribution functions via two self-consistent sets of equations is
given. By comparing with the traditional CCM and with Arponen's extension, it
is shown that the former is equivalent to a linear approximation to one set of
distribution functions and the later is equivalent to a random-phase
approximation to it. In additional to these two approximations, other
higher-order approximation schemes within the new formalism are also discussed.
As a demonstration, we apply this technique to a quantum antiferromagnetic spin
model.Comment: 15 pages. Submitted to Phys. Rev.
Increased target volume and hydrogen content in [11C]CH4 production
Introduction
High starting radioactivity is usually advantageous for producing radiopharmaceuticals with high specific radioactivity. However, the [11C]CH4 yields from N2-H2 gas target fall short from theoretical amounts, as calculated from the cross section for the well-known 14N(p,α)11C nuclear reaction1. The beneficial effect of increased target chamber temperature on [11C]CH4 yields has recently been brought forward by us2 and others3. In addition to the temperature effect, our attention has also been on the hydrogen content factor.
This study intends to examine the N2-H2 target performance in a substantially larger target chamber and at higher temperatures than our setup before and compare the results to the existing data.
Materials and Methods
Aluminium bodied custom design target chamber is used in fixed 17 MeV proton beam irradiations. Target chamber is equipped with heating elements and cooling circuit for temperature control. In addition to the target chamber body temperature, the target gas loading pressure and irradiation current can be varied.
The irradiation product is collected into an ad-sorbent trap that was immersed in a liquid argon cooling bath within a dose calibrator.
Results and Conclusion
Pursued data will show [11C]CH4 saturation yields (Ysat [GBq/µA]) at different irradiation and target parameters
Phase transition in the transverse Ising model using the extended coupled-cluster method
The phase transition present in the linear-chain and square-lattice cases of
the transverse Ising model is examined. The extended coupled cluster method
(ECCM) can describe both sides of the phase transition with a unified approach.
The correlation length and the excitation energy are determined. We demonstrate
the ability of the ECCM to use both the weak- and the strong-coupling starting
state in a unified approach for the study of critical behavior.Comment: 10 pages, 7 eps-figure
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 -- model for the linear chain, and we show
that we are able to reproduce exactly the dimerized ground (ket) state at
. The dimerized phase is stable over a range of values for
around 0.5. We present evidence of symmetry breaking by considering
the ket- and bra-state correlation coefficients as a function of . 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 CaVO (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
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
Renormalization of Hamiltonian Field Theory; a non-perturbative and non-unitarity approach
Renormalization of Hamiltonian field theory is usually a rather painful
algebraic or numerical exercise. By combining a method based on the coupled
cluster method, analysed in detail by Suzuki and Okamoto, with a Wilsonian
approach to renormalization, we show that a powerful and elegant method exist
to solve such problems. The method is in principle non-perturbative, and is not
necessarily unitary.Comment: 16 pages, version shortened and improved, references added. To appear
in JHE
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