The quantum Heisenberg antiferromagnet on the Sierpinski Gasket: An exact diagonalization study

Abstract

We present an exact diagonalization study of the quantum Heisenberg antiferromagnet on the fractal Sierpinski gasket for spin quantum numbers s=1/2,s=1 and s=3/2. Since the fractal dimension of the Sierpinski gasket is between one and two we compare the results with corresponding data of one- and two-dimensional systems. By analyzing the ground-state energy, the low-lying spectrum, the spin-spin correlation and the low-temperature thermodynamics we find arguments, that the Heisenberg antiferromagnet on the Sierpinski gasket is probably disordered not only in the extreme quantum case s=1/2 but also for s=1 and s=3/2. Moreover, in contrast to the one-dimensional chain we do not find a distinct behavior between the half-integer and integer-spin Heisenberg models on the Sierpinski gasket. We conclude that magnetic disorder may appear due to the interplay of frustration and strong quantum fluctuations in this spin system with spatial dimension between one and two.

12 pages (LaTeX), 7 figures, 3 tables, to appear in Physica A

Cited by in corpus (6)

• Classical percolation transition in the diluted two-dimensional S=1/2 Heisenberg antiferromagnet
• Quantum magnetism in two dimensions: From semi-classical Néel order to magnetic disorder
• Quantum dimer model with extensive ground-state entropy on the kagome lattice
• Phase Transition of the Ising Model on Fractal Lattice
• Magnetic order in spin-1 and spin-3/2 interpolating square-triangle Heisenberg antiferromagnets
• Ground state of composite bosons in low-dimensional graphs