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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
Award ID(s):
2037263
NSF-PAR ID:
10472007
Author(s) / Creator(s):
; ;
Publisher / Repository:
International Press
Date Published:
Journal Name:
Communications in mathematical sciences
Volume:
21
Issue:
5
ISSN:
1945-0796
Page Range / eLocation ID:
1447-1453
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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