Machine learning many-electron wave functions via backflow transformations

2020 Journal Club for Condensed Matter Physics  
The goal of determining the electronic structure of molecules and materials by solving the many-body Schrödinger equation has challenged theoretical physics and chemistry over the last century and driven the development of powerful approximations and computational methods. In the three papers above [1, 2, 3], the authors show how deep learning architectures can systematically improve many-body wave functions for Quantum Monte Carlo calculations, and benchmark their accuracy on the Hubbard model
more » ... [1], and for light atoms and small molecules [2, 3] . Out of several recent approaches for machine learning quantummany-body wave functions, e.g. [4, 5, 6, 7] , I have chosen these three papers biased by the common underlying strategy taken there to explore, extend, and possibly exhaust existing structures of many-body trial wave functions based on backflow transformations employing neural networks. The variational principle for the ground state energy, E 0 ≤ dRΨ * T (R)HΨ T (R), provides a simple, but powerful tool to obtain upper bounds for the ground state energy, E 0 , of any Hamiltonian H. Combined with Monte Carlo methods to evaluate the highly dimensional integral over all particle coordinates, variational and quantum Monte Carlo calculations have provided most accurate values of the many-body Schrödinger equation [8, 9] , only limited by the quality of the underlying trial wave function, Ψ T (R), for N fermions, R ≡ (r 1 , . . . , r N ). Can representations based on neural networks reduce this remaining bias similar successful 1
doi:10.36471/jccm_may_2020_01 fatcat:wrfr6xvihvhrzcdemurzxhcrly