In a tensor train approximation, the choice of the ordering can highly influence the accuracy of the representation. For spin chain models, the simple interaction picture gives a natural order, but in quantum chemistry, interactions are more intricate making difficult the choice of good ordering. In this talk, a new ordering scheme is proposed based on the discovery of an inversion symmetry of higher-order singular values for ground states of noninteracting Hamiltonians. This symmetry gives a natural criterion to optimize the tensor train representation.
Numerical experiments on model systems will be presented comparing our approach with the canonical and the Fiedler orders. The latter is based on an entanglement analysis of the ground-state and is widely used in practice. This is a joint work with Gero Friesecke (TU Munich).
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