Evaluation of low-energy effective Hamiltonian techniques for coupled spin triangles

Details Evaluation of low-energy effective Hamiltonian techniques for coupled spin triangles Evaluation of low-energy effective Hamiltonian techniques for coupled spin triangles

2000-02-07

arxiv.org/abs/cond-mat/0002099v1

Phys. Rev. B 62 (2000) 9484-9492

Physics

Condensed Matter

Strongly Correlated Electrons

Revtex, 11 pages, 11 eps figures

Scientific paper

10.1103/PhysRevB.62.9484

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.

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