From real materials to model Hamiltonians with density matrix downfolding

TL;DR

This paper introduces a formal theory called density matrix downfolding (DMD) that extracts effective Hamiltonians from first-principles many-body simulations, aiding in understanding complex materials.

Contribution

It develops a formal framework for downfolding that uses reduced density matrices to derive simplified models from detailed first-principles calculations.

Findings

Provides a systematic method for extracting effective Hamiltonians.

Connects wave function sampling to model Hamiltonian fitting.

Facilitates analysis of realistic materials with complex interactions.

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).