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 J_2 between triangles to the coupling J_1 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 is accurate only for the ground state for
rather low values of the ratio J_2 / J_1 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
excited states lying close to the ground state.Comment: Revtex, 11 pages, 11 eps figure