Using Higher-Order Singular Value Decomposition To Define Weakly Coupled and Strongly Correlated Clusters: The n-Body Tucker Approximation.

Abstract

An approximate wave function 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 occurring between limited numbers of clusters at a time. In this initial study, we 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. 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.