Simple Fermionic backflow states via a systematically improvable tensor decomposition

Abstract Strongly correlated electrons give rise to an array of electronic properties increasingly exploited in many emerging materials and molecular processes. However, the reliable numerical simulation of this quantum many-body problem still poses an outstanding challenge, in particular when accounting for the fermionic statistics of electrons. In this work, we introduce a compact and systematically improvable fermionic wave function based on a CANDECOMP/PARAFAC (CP) tensor decomposition of backflow correlations in second quantization. This ansatz naturally encodes many-electron correlations without the ordering dependence of other tensor decompositions. We benchmark its performance against standard models, demonstrating improved accuracy over comparable methods in Fermi-Hubbard and molecular systems and competitive results with state-of-the-art density matrix renormalization group (DMRG) in ab initio 2D hydrogenic lattices. By considering controllable truncations in the rank and range of the backflow correlations, as well as screening the local energy contributions for realistic Coulomb interactions, we obtain a scalable and interpretable approach to strongly correlated electronic structure problems that bridges tensor factorizations and machine learning-based representations.