Perturbation theory for strongly frustrated finite spin systems.

摘要

The topic of this study is the magnetic properties of closed clusters. The first issue addressed is the connection between magnetic properties and connectivity in essentially exact solutions of S = ½ quantum spin clusters. The second is the effect of magnetic anisotropy in a cluster on spin coherence.; The first issue is investigated for a set of model systems whose magnetic properties have strong dependence on connectivity at the classical approximation [1, 2]. The magnetization or its first derivative has a discontinuity as a function of applied field, depending on the number of sites in the system. The question I address is whether this dependence on connectivity survives in exact solutions for S = ½ clusters.; An effective Hamiltonian for degenerate states derived from classical ground states is calculated as a power series in the strength of quantum fluctuations, λ. These series converge asymptotically and are summed using Padé approximants. I have found that this dependence of magnetization on the number of sites is reflected in the analytic structure of the ground state energies and wavefunctions as functions of λ. This study exploits the use of large scale computing facilities to carry out high-precision perturbation expansions to high orders, ∼200–300.; The second issue investigated is the influence of magnetic anisotropy on magnetic clusters which are complexes of Fe, Mn and V atoms and behave as groups of up to 15 magnetic moments isolated from one another in crystals [3, 4]. These clusters have interesting magnetic properties and, most recently, it has been shown how one of them could be exploited as a qubit, a bit for a quantum computer [5].; I investigate a model for V₁₅, a complex of 15 S = ½ Vanadium atoms. The model includes a Heisenberg term and a symmetry allowed Dzyaloshinskii-Moriya (DM) interaction. I calculate the properties of this model as a function of temperature and external field using perturbation theory. By comparing with data I evaluate the parameters of the DM interaction. I show that this magnetic anisotropy term is an intrinsic source of decoherence for moments induced by external fields even at zero temperature.