Importance truncation in non-perturbative many-body techniques

Understand

Expansion many-body methods correspond to solving complex tensor networks.

• The (iterative) solving of the network and the (repeated) storage of the unknown tensors requires a computing power growing polynomially with the size of basis of the one-body Hilbert space one is working with.
• Thanks to current computer capabilities, ab initio calculations of nuclei up to mass $A\sim100$ delivering a few percent accuracy are routinely feasible today.
• However, the runtime and memory costs become quickly prohibitive as one attempts (possibly at the same time) (i) to reach out to heavier nuclei, (ii) to employ symmetry-breaking reference states to access open-shell nuclei and (iii) to aim for yet a greater accuracy.