Bridging simulations and theories of correlated electron materials using ideas from machine learning

There has historically been a tension between first principles calculations, which attempt to solve a realistic model while controlling approximations, and effective Hamiltonians, which attempt to condense the important physics into a simple enough model to solve without approximation. I will report on a research program that has, without approximation, recast the effective Hamiltonian as a compressed representation of the first principles Hamiltonian in a subspace, in a similar way that a JPEG file achieves a parsimonious description of a picture. Just as in the case of images, it turns out that concepts from data science and machine learning can help us describe complex effective Hamiltonians and choose, from first principles, the most accurate and parsimonious effective Hamiltonians.