Large-scale numerical investigations of the antiferromagnetic Heisenberg icosidodecahedron

Abstract

a b s t r a c tWe present up to date investigations of the antiferromagnetic Heisenberg icosidodecahedron by means of the density matrix renormalization group method. We compare our results with modern correlator product state as well as Lanczos calculations.

The antiferromagnetic $S=1/2$ Heisenberg model on the C$_{60}$ fullerene geometry

“…Thus we conclude that as long as the numbering of the sites is reasonable and more or less minimizes the hopping distances, the dependence on the numbering itself is small and an inaccuracy that results from a suboptimal numbering can simply be compensated by moderately increasing the bond dimension. This is in line with the conclusions of Ummethum, Schnack and Läuchli [29]. Finally, we note that by checking the energy variance (Eq.…”

“…A random permutation of the sites, on the other hand, leads to a representation with a large MPO bond dimension which the compression algorithm is unable to decrease, and the convergence becomes much worse. For a benchmark with a system solvable by exact diagonalization, we compare a similar spiral mapping for the icosidodecahedron with the mapping used by Exler and Schnack [29,44] and find that both approaches come within 99.97% of the exact S = 1/2 ground-state energy [22] at a bond dimension of χ SU(2) = 500. Thus we conclude that as long as the numbering of the sites is reasonable and more or less minimizes the hopping distances, the dependence on the numbering itself is small and an inaccuracy that results from a suboptimal numbering can simply be compensated by moderately increasing the bond dimension.…”

“…The former has only triangular plaquettes, the latter only pentagonal ones, and both are small enough to be solved by full diagonalization if spatial symmetries are exploited to reduce the Hilbert space size [26]. I h also has 5 members within the Archimedean solids, of which the icosidodecahedron with 30 sites (triangular and pentagonal faces) has been the subject of particularly intense study [27][28][29][30][31], since this is the geometry of the magnetic atoms in the Keplerate molecules {Mo 72 V 30 }, {Mo 72 Cr 30 } and {Mo 72 Fe 30 }, with S = 1/2, 3/2 and 5/2 respectively [32][33][34]. It is solvable by exact diagonalization for S = 1/2 [27].…”

Magnetocaloric Effect in Cu5-NIPA Molecular Magnet: A Theoretical Study

“…The calculations become more even more demanding when structures involving high number of spins, especially S > 1/2, are modeled. For this purpose, advanced and effective close-toexact approaches for thermodynamic description of the spin systems are developed [52][53][54][55].…”

Magnetization distribution in a spin ladder-shaped quantum nanomagnet

“…We can mention that the theoretical studies of magnetization distribution (performed with either exact or approximate methods) are known in the literature both for zero-dimensional magnets [36] as well as for other non-uniform systems, like, for example, thin films [37][38][39]. Also the thermodynamics of magnetic clusters was subject of several computational works exploiting the exact (or close to exact) approaches, involving both 'classical', Isingbased systems [40][41][42][43][44][45] as well as highly non-trivial quantum Heisenberg systems [7,40,[46][47][48][49][50][51][52][53][54][55][56].…”