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 journalArticle

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).

Original languageEnglish (US)
Article number43
JournalFrontiers in Physics
Volume6
Issue numberMAY
DOIs
StatePublished - May 11 2018

Fingerprint

Hamiltonians
Density Matrix
Hilbert spaces
Wave functions
Computer hardware
Simulation
First-principles Calculation
simulation
Hilbert space
Complications
Physical Model
Wave Function
leaves
hardware
Subspace
Hardware
wave functions
Model
Term
Energy

Keywords

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

ASJC Scopus subject areas

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

Cite this

From real materials to model Hamiltonians with density matrix downfolding. / Zheng, Huihuo; Changlani, Hitesh J.; Williams, Kiel T.; Busemeyer, Brian; Wagner, Lucas K.

In: Frontiers in Physics, Vol. 6, No. MAY, 43, 11.05.2018.

Research output: Contribution to journalArticle

Zheng, Huihuo ; Changlani, Hitesh J. ; Williams, Kiel T. ; Busemeyer, Brian ; Wagner, Lucas K. / From real materials to model Hamiltonians with density matrix downfolding. In: Frontiers in Physics. 2018 ; Vol. 6, No. MAY.
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