Fundamental Building Blocks of Strongly Correlated Wave Functions
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The calculation of realistic N-body wave functions for identical fermions is still an open problem in physics, chemistry, and materials science, even for N as small as two. A recently discovered fundamental algebraic structure of many-body Hilbert space allows an arbitrary many-fermion wave function to be written in terms of a finite number of antisymmetric functions called shapes. Shapes naturally generalize the single-Slater-determinant form for the ground state to more than one dimension. Their number is exactly N! d−1 in d dimensions. An efficient algorithm is described to generate all fermion shapes in spaces of odd dimension, which improves on a recently published general algorithm. The results are placed in the context of contemporary investigations of strongly correlated electrons.
KeywordsStrong correlations Many-body wave functions Invariant theory
I thank D. Svrtan for his help and interest.
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