Evaluation of low-energy effective Hamiltonian techniques for coupled spintriangles

Motivated by recent work on Heisenberg antiferromagnetic spin systems on va rious lattices made up of triangles, we examine the low-energy properties o f a chain of antiferromagetically coupled triangles of half-odd-integer spi ns. We derive the low-energy effective Hamiltonian to second order in the r atio of the coupling J(2) between triangles to the coupling J(1) within eac h triangle. The effective Hamiltonian contains four states for each triangl e which are given by the products of spin-1/2 states with the states of a p seudospin 1/2. We compare the results obtained by exact diagonalization of the effective Hamiltonian with those obtained for the full Hamiltonian usin g exact diagonalization and the density-matrix renormalization group method . It is found that the effective Hamiltonian gives an accurate value for th e ground-state energy only if the ratio J(2)/J(1) is less than about 0.2 an d 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 tha n in the spin-1/2 case. Finally, we have studied nonlinear topologies where the LEH results deviate further from the exact results.