The anisotropic quantum antiferromagnet on the Sierpinski gasket: Ground state and thermodynamics
arXiv:cond-mat/0403147 · doi:10.1140/epjb/e2004-00098-8
Abstract
We investigate an antiferromagnetic s=1/2 quantum spin system with anisotropic spin exchange on a fractal lattice, the Sierpinski gasket. We introduce a novel approximative numerical method, the configuration selective diagonalization (CSD) and apply this method to the Sierpinski 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 Sierpinski gasket shows a disordered magnetic ground state with a very short correlation length of about 1 and an, albeit very small, spin gap. This conclusion holds for Heisenberg as well a for XY exchange.
LaTeX: 16 pages, 9 figures, 1 table