  We have studied the properties of the giant Keplerate molecular magnet
Mo72Fe30, as a function of applied magnetic field, using the correlator product
state (CPS) tensor network ansatz. The magnet is modeled with an S = 5/2
antiferromagnetic Heisenberg Hamiltonian on the 30-site icosidodecahedron
lattice, a model for which exact diagonalization is infeasible. The CPS ansatz
produces significant improvements in variational energies relative to previous
studies using the density matrix renormalization group, a result of its
superior ability to handle strong correlation in two dimensional spin systems.
The CPS results reaffirm that the ground state energies adhere qualitatively to
the parabolic progression of the rotational band model (RBM), but show
important deviations near 1/3 of the saturation field. These deviations predict
anomalous behavior in the differential magnetization and heat capacity that
cannot be explained by the RBM alone. Finally, we show that these energetic
deviations originate from a qualitative change in the ground state that
resembles a finite size analogue of a phase transition.
