The quantum Heisenberg antiferromagnet on the Sierpi ski gasket: an exact diagonalization study

We present an exact diagonalization study of the quantum Heisenberg antiferromagnet on the fractal Sierpi ski gasket for spin quantum numbers and . Since the fractal dimension of the Sierpi ski gasket is between 1 and 2, we compare the results with the 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 Sierpi ski gasket is probably disordered not only in the extreme quantum case , but also for s=1 and . 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 Sierpi ski 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 1 and 2.