https://doi.org/10.1140/epjb/e2004-00098-8
The anisotropic quantum antiferromagnet on the Sierpiński gasket: Ground state and thermodynamics
1
Center for Simulational Physics, Department of Physics and Astronomy,
University of Georgia, Athens GA 30602, USA
and Max-Planck-Institut Magdeburg, Sandtorstr.1, 39106 Magdeburg, Germany
2
Forschungszentrum Karlsruhe, Institut für Nanotechnologie,
Postfach 3640, 76021 Karlsruhe, Germany
3
Otto-von-Guericke-Universität Magdeburg,
Institut für Theoretische Physik,
PF 4120, 39106 Magdeburg, Germany
4
Uniwersytet im. Adama Mickiewicza, Wydział Fizyki,
ul.Umultowska 85, 61-614 Poznań, Poland
Corresponding author: a voigt@mpi-magdeburg.mpg.de
Received:
8
December
2003
Revised:
18
February
2004
Published online:
20
April
2004
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 Sierpińskigasket 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 Sierpińskigasket shows a disordered magnetic ground state with a
very short correlation length of 
and an, albeit very
small, spin gap. This conclusion holds for Heisenberg as well a for XY
exchange.
PACS: 75.10.-b – General theory and models of magnetic ordering / 05.45.Df – Fractals / 75.40.Mg – Numerical simulation studies
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004
