An approximate wavefunction ansatz is presented which describes low-energy states of a highly clustered molecular system as a linear combination of multiple reduced-rank tensors. Using the Tucker decomposition as a way to obtain local clusters states, the exact solution is solved for in the space spanned by a small number of states on each cluster, with complete correlation occuring between limited numbers of clusters at a time. In this talk, I will report the implementation for a Heisenberg spin Hamiltonian with numerical examples of regular grid spin lattices, and ab initio-derived spin-Hamiltonians used to analyze the approximation. In addition to the exact (variational) determination of the coefficient tensors, we will also explore the possibility of using perturbation theory and strategies based on the coupled electron-pair approximation. From these results, we find that the proposed method works well when the Hamiltonian interactions within a cluster are larger than between a cluster, and when this is not true, the method is not effective.

Using higher-order singular value decomposition to define weakly coupled and strongly correlated clusters: the <i>n</i>-body Tucker approximation

255th National Meeting (2018)

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Using higher-order singular value decomposition to define weakly coupled and strongly correlated clusters: the n-body Tucker approximation