This is a research code to investigate the use of deep learning to map between various properties of lattice systems. In particular, the code can learn the mapping from the local density to the wave function and other ground-state properties. This mapping from the density to the wave function is the map known to exist from the Hohenberg-Kohn theorem.

This code is in development. It currently uses the one-dimensional Hubbard model and spinless Hubbard model. The spinless system has been studied using similar approaches in the following papers:

Javier Robledo Moreno, Giuseppe Carleo, Antoine Georges, Physical Review Letters 125, 076402 (2020)

M. Michael Denner, Mark H. Fischer, Titus Neupert, Physical Review Research 2, 033388 (2020)

The code can generate its own training data, which is obtained by applying random potentials to a given lattice model.

The code uses PyTorch and a small number of other standard libraries. The startup and input system uses Abseil. Flags can be specified on the command line or in a config file, for example:

python3 deep_hk/main.py --flagfile=input.cfg

Example config files are given in the examples directory, and the available flags can be viewed with

python3 deep_hk/main.py --help

Alternatively, a training script can be written directly, with examples given in the examples/hubbard/ directoy.

Also provided is a short tutorial as a Jupyter notebook, available in the examples directory.