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Title: Geometry of backflow transformation ansatze for quantum many-body fermonic wavefunctions
Wave function ansatze based on the backflow transformation are widely used to parametrize anti-symmetric multivariable functions for many-body quantum problems. We study the geometric aspects of such ansatze, in particular we show that in general totally antisymmetric polyno- mials cannot be efficiently represented by backflow transformation ansatze at least in the category of polynomials. In fact, if there are $N$ particles in the system, one needs a linear combination of at least $O(N^{3N−3})$ determinants to represent a generic totally antisymmetric polynomial. Our proof is based on bounding the dimension of the source of the ansatze from above and bounding the dimension of the target from below.  more » « less
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International Press
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Communications in mathematical sciences
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Medium: X
Sponsoring Org:
National Science Foundation
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