Fitting effective models using QMC parameter derivatives

Effective models are fundamental to our understanding of complex materials, but selecting the right model and parameters to accurately describe a particular material can be challenging. The recently developed density matrix downfolding method (DMD) [1] uses an ensemble of quantum Monte Carlo calculations to both select and fit parameters to effective models for materials. However, this method is computationally extremely demanding. In a similar spirit to force matching in classical model fitting [2], we improve the efficiency of DMD by computing derivatives of the energy and density matrix with respect to parameters of each trial wave function. We demonstrate the new technique by computing a band structure for silicon using first principles quantum Monte Carlo.

[1] H. Zheng, H. J. Changlani, K. T. Williams, B. Busemeyer, and L. K. Wagner, Front. Phys. 6, 43 (2018).
[2] F. Ercolessi and J. B. Adams, Europhys. Lett. 26, 583 (1994).