Tensor hypercontraction: A universal technique for the resolution of matrix elements of local, finite-range $N$-body potentials in many-body quantum problems

TL;DR

The paper introduces X-THC, a tensor hypercontraction method that efficiently factorizes matrix elements of local, finite-range N-body potentials, significantly reducing computational costs in quantum many-body simulations.

Contribution

It develops the X-THC technique for separable tensor factorization of N-body potential matrix elements, enabling faster quantum many-body calculations.

Findings

Provides a highly separable tensor factorization of N-body potentials.

Achieves substantial computational savings in quantum physics simulations.

Facilitates efficient handling of exchange-like contractions.

Abstract

Configuration-space matrix elements of N-body potentials arise naturally and ubiquitously in the Ritz-Galerkin solution of many-body quantum problems. For the common specialization of local, finite-range potentials, we develop the eXact Tensor HyperContraction (X-THC) method, which provides a quantized renormalization of the coordinate-space form of the N-body potential, allowing for a highly separable tensor factorization of the configuration-space matrix elements. This representation allows for substantial computational savings in chemical, atomic, and nuclear physics simulations, particularly with respect to difficult "exchange-like" contractions.