Effective models derived for the hydrogen chain using correlated many-body wave functions*

It is challenging in first-principles calculations to elucidate the mechanisms underlying phase transitions in complicated materials where multiple interactions, such as electron-electron and electron-phonon interactions, play essential roles. With the help of model Hamiltonians, one can isolate specific interaction channels and study how they compete or collaborate to generate the plethora of phases. This work proposes a general procedure to derive accurate interacting Hamiltonians in a simple system, the hydrogen chain, using correlated many-body wave functions generated using fixed-node diffusion Monte Carlo. We show that the effective on-site Coulomb repulsion $U$ and double occupancy compensate and give rise to a nearly constant on-site interaction contribution to the total energy during dimerization. Our results show that the electron hoppings contribute to the energy drop the most when the chain dimerizes. This work lays out the workflow of deriving models using the highly accurate first-principles method and demonstrates how to establish causation of certain effective interactions during phase transition.