Quantum Physics Division
Faculty of PhysicsAdam Mickiewicz University

The quantum Heisenberg antiferromagnet on the Sierpiński gasket” an exact diagonalization study

A. Voigt1 , J. Richter2 , P. Tomczak3

1 Department of Physics and Astronomy, Center for Simulational Physics, University of Georgia, Athens GA 30605 USA
2 Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, PF 4120, 39106 Magdeburg, Germany
3 Department of Physics, Adam Mickiewicz University, ul. Umultowska 85, 61-614, Poznań , Poland

Physica A, 299, 461-474 (2001)
DOI: 10.1016/S0378-4371(01)00318-1


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.


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