A Quantum Monte Carlo Study of Quantum Materials in the Intermediate Correlation Regime

Clio Johnson

Published Sep 14, 2026• 0 citations

Abstract

Variational and diffusion Monte Carlo (VMC and DMC) are widely used techniques in the Monte Carlo study of many-body quantum systems. Through efficient use of ran- dom sampling to solve many-dimensional integrals, they can be used to reliably solve the Schrödinger equation. Within the wider ecosystems of electronic structure calculation, quantum chemistry, and quantum simulation, quantum Monte Carlo (QMC) methods are used in tandem with density functional theory (DFT) and other computational methods to deliver insight into a vast array of condensed matter systems. Of particular interest to this work are systems in the intermediate correlation regime, where methods such as simple band theory and the Hubbard model break down. This thesis proposes and tests an explicit three-body backflow term to improve the accuracy of VMC and DMC calculations by incorporating higher-order correlation in order to reduce fixed-node er- ror in DMC, finding statistically significant improvements in ground state energies and improved variance in a water molecule. Then, QMC is used to calculate accurate charge densities for weak and intermediately correlated materials, to test commonly used dens- ity functional approximations in a controlled environment, providing insight into where these approximations perform well, and where they fail. Finally, DMC is used to generate ground state energy data for a dipolar Fermi gas of dressed Rydberg atoms interacting in the intermediate correlation regime. This data is parametrised in terms of interaction strength, for use in generating exchange-correlation functionals, to enable the DFT study of inhomogeneous systems of dressed Rydberg atoms.

DOI: 10.17635/lancaster/thesis/3411

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