Motivated by recent work on Heisenberg antiferromagnetic spin systems on various lattices made up of triangles, we examine the low-energy properties of a chain of antiferromagnetically coupled triangles of half-odd-integer spins. We derive the low-energy effective Hamiltonian to second order in the ratio of the coupling
J2 between triangles to the coupling
J1 within each triangle. The effective Hamiltonian contains four states for each triangle which are given by the products of spin-1/2 states with the states of a pseudospin 1/2. We compare the results obtained by exact diagonalization of the effective Hamiltonian with those obtained for the full Hamiltonian using exact diagonalization and the density-matrix renormalization group method. It is found that the effective Hamiltonian gives an accurate value for the ground-state energy only if the ratio
J2/J1 is less than about 0.2 and that too for the spin-1/2 case with linear topology. The chain of spin-1/2 triangles shows interesting properties like spontaneous dimerization and several singlet and triplet low-energy (possibly gapless) states which lie close to the ground state. We have also studied the spin-3/2 case and find the low-energy effective Hamiltonians (LEH's) to be less accurate there than in the spin-1/2 case. Finally, we have studied nonlinear topologies where the LEH results deviate further from the exact results.
Low-lying excited states of the spin-1 antiferromagnetic Heisenberg chain with a spin- S ( S >1) impurity are investigated by means of variational method. It is shown that (1) the phenomenological Hamiltonian which may be useful in the analysis of the experimental results can be derived from the usual Hamiltonian, (2) the origin of the anisotropy in the phenomenological Hamiltonian can be explained from the results obtained by the analytical method, (3) the impurity spin brings about a massive mode in the Haldane gap, (4) the energy levels of the massive mode can be classified into four multiples corresponding to the states with the total spin quantum S = S +1, S and S -1 coupled to triplet of host-system and the state with S = S coupled to the singlet of host-system.
While the diagonalization of a quadratic bosonic form can always be done using a Bogolyubov transformation, the practical implementation for systems with a large number of different bosons is a tedious analytical task.Here we use the coupled cluster method to exactly diagonalise such complicated quadratic forms.This yields to a straightforward algorithm which can easily be implemented using computer algebra even for a large number of different bosons.We apply this method on a Heisenberg system with two interpenetrating square lattice antiferromagnets, which is a model for the quasi-2D antiferromagnet Ba 2 Cu3 O 4 Cl2 .Using a four-magnon spin wave approximation we get a complicated Hamiltonian with four different bosons, which is treated with coupled cluster method.Results are presented for magnetic ground state correlations.