Speaker:
Di Luo (University of Illinois, Urbana-Champaign)
Backflow Transformations via Neural Networks for Quantum Many-Body Wave Functions
Obtaining an accurate ground state wave function is one of the great challenges in the quantum many-body problem. In our recent work [1], we propose a new class of wave functions for Fermion, neural network backflow (NNB). The backflow approach, pioneered originally by Feynman, adds correlation to a mean-field ground state by transforming the single-particle orbitals in a configuration-dependent way. NNB uses a feed-forward neural network to learn the optimal transformation via variational Monte Carlo. It directly dresses a mean-field state, can be systematically improved and directly alters the sign structure of the wave-function. The standard backflow can be explicitly represented under NNB and further generalized to arbitrary lattice. We benchmark the NNB on a Hubbard model at intermediate doping, finding that it significantly decreases the relative error and restores the symmetry of both observables and single-particle orbitals.
[1]: Di Luo, Bryan K. Clark, Backflow Transformations via Neural Networks for Quantum Many-Body Wave-Functions, Phys. Rev. Lett. 122, 226401.