Density-Matrix Downfolding: A Systematically Improvable Approach to Material-Specific Effective Interacting Models

Among current ab-initio downfolding approaches, the constrained random phase approximation (cRPA) has been widely used to construct effective interactions from first-principles calculations. However, recent benchmark study [1] using state-of-the-art first-principles many-body wavefunction methods show that the downfolded model from DFT+cRPA can be sensitive to each downfolding step, motivating the need for a more accurate and systematically improvable approach. This talk introduces a new ab-initio downfolding approach, renormalized density matrix downfolding (R-DMD) that is based on real-space quantum Monte Carlo (QMC) data. The first part of the talk focuses on the formulation of R-DMD [2], where effective Hamiltonians are constructed by one-to-one mapping between the ab-initio and model eigenstates. Building on this, the second part introduces the configuration-motivated R-DMD, where the authors use efficiently targeted many-body wavefunctions to probe the low-energy landscape of the high-dimensional ab-initio Hilbert space in a data-driven yet physically grounded way, through a scan of all ab-initio states motivated by model configurations but dressed by bath electrons [3].  Benchmark results of this approach in ab-initio hydrogen chains show that one can systematically converge the model parameters with increasing supercell sizes. The method is then applied in real correlated materials—the correlated perovskite SrVO₃ and CaVO₃—where a three-band Hubbard-Kanamori model is obtained. This framework enables extraction of the underlying physics from high-dimensional QMC wavefunctions in a minimal and interpretable form. Moreover, this method yields effective models that are interpretable, material-specific, and based in systematically improvable ab-initio data, with direct applications to quantum embedding theory and impurity systems.

[1] Yueqing Chang, et al., npj Comput. Mater. 10, 129 (2024).

[2] Yueqing Chang, Sonali Joshi, Lucas K. Wagner, Phys. Rev. B 110, 195103 (2024).

[3] Yueqing Chang, et al., in preparation (2025).