C. Raghu et al., Properties of low-lying states in some high-nuclearity Mn, Fe, and V clusters: Exact studies of Heisenberg models - art. no. 064419, PHYS REV B, 6406(6), 2001, pp. 4419
Using an efficient numerical scheme that exploits spatial symmetries and sp
in parity, we have obtained the exact low-lying eigenstates of exchange Ham
iltonians for the high-nuclearity spin clusters, Mn-12, Fe-8, and V-15. The
largest calculation involves the Mn-12 cluster that spans a Fock space of
a hundred million. Our results show that the earlier estimates of the excha
nge constants need to be revised for the Mn-12 cluster to explain the level
ordering of low-lying eigenstates. In the case of the Fes cluster, correct
level ordering can be obtained, which is consistent with the exchange cons
tants for the already known clusters with butterfly structure. In the V-15
cluster, we obtain an effective Hamiltonian that reproduces exactly, the ei
ght low-lying eigenvalues of the full Hamiltonian.