The anisotropic quantum antiferromagnet on the Sierpiński gasket: Ground state and thermodynamics

We investigate an antiferromagnetic s=1/2 quantum spin system with anisotropic spin exchange on a fractal lattice, the Sierpiński gasket. We introduce a novel approximative numerical method, the configuration selective diagonalization (CSD) and apply this method to a the Sierpiński gasket with N=42. Using this and other methods we calculate ground state energies, spin gap, spin–spin correlations and specific heat data and conclude that the s=1/2 quantum antiferromagnet on the Sierpiński gasket shows a disordered magnetic ground state with a very short correlation length of ξ ≈ 1 and an, albeit very small, spin gap. This conclusion holds for Heisenberg as well a for XY exchange.