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Configuration-space matrix elements of N-body potentials arise naturally andubiquitously in the Ritz-Galerkin solution of many-body quantum problems. Forthe common specialization of local, finite-range potentials, we develop theeXact Tensor HyperContraction (X-THC) method, which provides a quantizedrenormalization of the coordinate-space form of the N-body potential, allowingfor a highly separable tensor factorization of the configuration-space matrixelements. This representation allows for substantial computational savings inchemical, atomic, and nuclear physics simulations, particularly with respect todifficult "exchange-like" contractions.

physical review letters

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