We investigate the quantum dynamics of the spins on different Heisenberg antiferromagnetic spin lattice systems. Firstly, we applied the coupledcluster method to the spin1/2 antiferromagnetic \emph{XXZ} model on a square lattice by employing an approximation which contains twobody longrange correlations and highorder fourbody local correlations. Improvement is found for the groundstate energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the twobody correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the highorder spinwave theory.Secondly, we study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic manybody approach based on magnondensity waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone $\Gamma(\mathbf q=0)$ and at the magnetic ordering wavevectors $\pm[\mathbf Q= (4\pi/3,0)]$, the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on twodimensional models may be considered as quasigapped, as any finitesize effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spinwave excitations. We have also investigated the excited states of the quasionedimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnondensity waves. A model Hamiltonian with a uniaxial singleion anisotropy is first studied by a spinwave theory based on the oneboson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearestneighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the noncollinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and noninteger spin quantum numbers, and we find good agreements after the higherorder contributions are included in our calculations.
Date of Award  31 Dec 2013 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  Yang Xian (Supervisor) 

 Heisenberg antiferromagnet, spin lattice systems,longitudinal excitations, coupledcluster, spinwave
Study of the excited states of the quantum antiferromagnets
Merdan, M. (Author). 31 Dec 2013
Student thesis: Phd