GEOMETRY OF BACKFLOW TRANSFORMATION ANSATZE FOR QUANTUM MANY-BODY FERMIONIC 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 polynomials 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(N3N−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.

Duke Scholars

Author Jianfeng Lu Mathematics