AUTHOR=Zheng Huihuo , Changlani Hitesh J. , Williams Kiel T. , Busemeyer Brian , Wagner Lucas K. TITLE=From Real Materials to Model Hamiltonians With Density Matrix Downfolding JOURNAL=Frontiers in Physics VOLUME=6 YEAR=2018 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2018.00043 DOI=10.3389/fphy.2018.00043 ISSN=2296-424X ABSTRACT=

Due to advances in computer hardware and new algorithms, it is now possible to perform highly accurate many-body simulations of realistic materials with all their intrinsic complications. The success of these simulations leaves us with a conundrum: how do we extract useful physical models and insight from these simulations? In this article, we present a formal theory of downfolding–extracting an effective Hamiltonian from first-principles calculations. The theory maps the downfolding problem into fitting information derived from wave functions sampled from a low-energy subspace of the full Hilbert space. Since this fitting process most commonly uses reduced density matrices, we term it density matrix downfolding (DMD).