CCQ Seminar: Javier Robledo Moreno

Tuesday Jun 9, 2020, 12:00 PM → 1:00 PM America/New_York

Title: Deep learning the Hohenberg-Kohn maps of Density Functional Theory

Abstract:
A striking consequence of the Hohenberg-Kohn theorem of density functional theory is the ex-
istence of a bijection between the local density and the ground-state many-body wave function. I will describe or recent work [1], where we study the problem of constructing approximations to the
Hohenberg-Kohn map using a statistical learning approach. Using supervised deep learning with
synthetic data, we show that this map can be accurately constructed for a chain of one-dimensional
interacting spinless fermions, in different phases of this model including the charge ordered Mott insulator and metallic phases. However, we also find that the learning is less effective across quan-
tum phase transitions, suggesting an intrinsic difficulty in efficiently learning non-smooth functional relations. We further study the problem of directly reconstructing complex observables from simple
local density measurements. In particular we study the reconstruction of density-density correlations and show that the machine-learned correlations can reproduce the finite-size scaling and Luttinger Liquid parameters of the system.