3 research outputs found
Diagrammatic approach in the variational coupled-cluster method
Recently, as demonstrated by an antiferromagnetic spin-lattice application,
we have successfully extended the coupled-cluster method (CCM) to a variational
formalism in which two sets of distribution functions are introduced to
evaluate Hamiltonian expectation. We calculated these distribution functions by
employing an algebraic scheme. Here we present an alternative calculation based
on a diagrammatic technique. Similar to the method of correlated-basis
functionals (CBF), a generating functional is introduced and calculated by a
linked-cluster expansion in terms of diagrams which are categorized and
constructed according to a few simple rules and using correlation coefficients
and Pauli exclusion principle (or Pauli line) as basic elements. Infinite
resummations of diagrams can then be done in a straightforward manner. One such
resummation, which includes all so-called ring diagrams and ignores Pauli
exclusion principle, reproduces spin-wave theory (SWT). Approximations beyond
SWT are also given. Interestingly, one such approximation including all
so-called super-ring diagrams by a resummation of infinite Pauli lines in
additional to resummations of ring diagrams produces a convergent, precise
number for the order-parameter of the one-dimensional isotropic model, contrast
to the well-known divergence of SWT. We also discuss the direct relation
between our variational CCM and CBF and discuss a possible unification of the
two theories.Comment: 18 pages, 9 figure
Excited states of quantum many-body interacting systems: A variational coupled-cluster description
We extend recently proposed variational coupled-cluster method to describe
excitation states of quantum many-body interacting systems. We discuss, in
general terms, both quasiparticle excitations and quasiparticle-density-wave
excitations (collective modes). In application to quantum antiferromagnets, we
reproduce the well-known spin-wave excitations, i.e. quasiparticle magnons of
spin . In addition, we obtain new, spin-zero magnon-density-wave
excitations which has been missing in Anserson's spin-wave theory. Implications
of these new collective modes are discussed.Comment: 17 pages, 4 figure
Longitudinal excitations in quantum antiferromagnets
By extending our recently proposed magnon-density-waves to low dimensions, we
investigate, using a microscopic many-body approach, the longitudinal
excitations of the quasi-one-dimensional (quasi-1d) and quasi-2d Heisenberg
antiferromagnetic systems on a bipartite lattice with a general spin quantum
number. We obtain the full energy spectrum of the longitudinal mode as a
function of the coupling constants in the original lattice Hamiltonian and find
that it always has a non-zero energy gap if the ground state has a long-range
order and becomes gapless for the pure isotropic 1d model. The numerical value
of the minimum gap in our approximation agrees with that of a longitudinal mode
observed in the quasi-1d antiferromagnetic compound KCuF at low
temperature. It will be interesting to compare values of the energy spectrum at
other momenta if their experimental results are available.Comment: 19 pages, 4 figure