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

Raghu, C and Rudra, Indranil and Ramasesha, S and Sen, Diptiman (2000) Evaluation of low-energy effective Hamiltonian techniques for coupled spin triangles. In: Physical Review B, 62 (14). pp. 9484-9492.

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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 gives an accurate value for the ground-state energy only if the ratio $J_2/J_1$ 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.

Item Type: Journal Article
Publication: Physical Review B
Publisher: American Institute of Physics
Additional Information: Copyright of this article belongs to American Institute of Physics.
Department/Centre: Division of Chemical Sciences > Solid State & Structural Chemistry Unit
Division of Physical & Mathematical Sciences > Centre for Theoretical Studies (Ceased to exist at the end of 2003)
Date Deposited: 01 Sep 2006
Last Modified: 19 Sep 2010 04:30
URI: http://eprints.iisc.ac.in/id/eprint/8131

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