ct7b00696_si_003.txt (165.89 kB)
Using Higher-Order Singular Value Decomposition To Define Weakly Coupled and Strongly Correlated Clusters: The n‑Body Tucker Approximation
dataset
posted on 2017-08-22, 00:00 authored by Nicholas J. MayhallAn 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.