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We study the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on a series offinite-size clusters with features inspired by the fullerenes. Frustration dueto the presence of pentagonal rings makes such structures challenging in thecontext of quantum Monte-Carlo methods. We use an exact diagonalizationapproach combined with a truncation method in which only the most importantbasis states of the Hilbert space are retained. We describe an efficientvariational method for finding an optimal truncation of a given size whichminimizes the error in the ground state energy. Ground state energies andspin-spin correlations are obtained for clusters with up to thirty-two siteswithout the need to restrict the symmetry of the structures. The results arecompared to full-space calculations and to unfrustrated structures based on thehoneycomb lattice.Comment: 22 pages and 12 Postscript figure

Variational Hilbert-space-truncation approach to quantum Heisenberg antiferromagnets on frustrated clusters