From real materials to model Hamiltonians with density matrix downfolding

Huihuo Zheng, Hitesh J. Changlani, Kiel T. Williams, Brian Busemeyer, Lucas K. Wagner

Research output: Contribution to journalArticlepeer-review


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).

Original languageEnglish (US)
Article number43
JournalFrontiers in Physics
Issue numberMAY
StatePublished - May 11 2018


  • Downfolding
  • Effective model
  • Machine learning
  • Quantum Monte Carlo
  • Strongly correlated systems

ASJC Scopus subject areas

  • Biophysics
  • Materials Science (miscellaneous)
  • Mathematical Physics
  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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