Deep learning the Hohenberg-Kohn maps of Density Functional Theory

Understand

A striking consequence of the Hohenberg-Kohn theorem of density functional theory is the existence of a bijection between the local density and the ground-state many-body wave function.

• Here 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 and the critical point separating them.
• However, we also find that the learning is less effective across quantum phase transitions, suggesting an intrinsic difficulty in efficiently learning non-smooth functional relations.