Low-lying excitations and thermodynamics of an antiferromagnetic Heisenberg fractal system of a dimension between one and two

Abstract

We investigate a frustrated Heisenberg spin-1/2 antiferromagnet on a fractal lattice of dimension d=ln3/ln2 (Sierpinski gasket). Calculations were performed using (a) exact diagonalization of all eigenstates and eigenvectors for systems up to N=15 and (b) the Decoupled-Cell Quantum-Monte-Carlo method for systems up to N=366. We present the low-lying spectrum and the specific heat. The specific heat shows a second maximum in the low-temperature region. This behavior is similar to the behavior of the quantum Heisenberg antiferromagnet on a kagome lattice and suggests a disordered ground state and a spin gap in the considered system.