The major obstacle of using low-rank tensor approximation for many-electron wavefunctions in Hilbert space can generally be attributed to the antisymmetry, which can result in a factorial increase of ranks with respect to the number of electrons. Here we show how this problem can be circurmvented by using a 'stringly upper triangluar' representation. Numerical examples demonstrate that the many-electron wavefunctions in such representation are highly compressible, which implies that low-rank tensor network states can be employed as variational ansatz. As the simplest realization, the Hilbert-space matrix product states (HS-MPS) or tensor train representation is introduced, which has rich mathematical structures. The formal and numerical comparisons among the HS-MPS, the conventional Fock-space formulation, and configuration interactions (CI) are also made, which shed light on how many-electron wavefunctions may be approximated in an efficient way in terms of contraction/renormalization of many-body basis.&lt;!--EndFragment--&gt;

Low-rank tensor approximations for many-electron wavefunctions in Hilbert space

251st National Meeting (2016)

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