A route to systematically improveable effective Hamiltonians in condensed matter

Effective models of complex systems are fundamental to our understanding of matter. Traditionally, these models are developed either through direct phenomenological modeling of experiments, through heuristic interpretation of first principles calculations, or a combination of both. Typically the latter are based on density functional theory calculations, which contain inherent approximations that are difficult to overcome systematically. Fortunately, over much work in the past few decades, it has become possible to obtain highly accurate many-body solutions of first principles models of matter using techniques like quantum chemistry and quantum Monte Carlo. However, connecting these solutions to lower energy models has been a challenge.

I will present work on constructing a framework to allow for two main advances in the construction of effective Hamiltonians from first principles. (1) As the first principles solutions approach exact ones, the effective Hamiltonian should approach exact. (2) The effective Hamiltonians should be as simple as possible, including renormalization of variables in order to achieve simplicity. I will also go over several toy examples in which we benchmark standard embedding techniques using highly accurate data, including the derivation of spin models and embedded defect models.