Density Functional Theory and Variational Monte Carlo Calculations for 2-Dimensional Electron Systems

Clio Johnson

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.

Norman Henry March

Maziar Nekovee, W. M. C. Foulkes, A. J. Williamson +3 more

We present a new method for realizing the adiabatic connection approach in density functional theory, which is based on combining accurate variational quantum Monte Carlo calculations with a constrained optimization of the ground state many-body wavefunction for different values of the Coulomb coupling constant. We use the method to study an electron gas in the presence of a cosine-wave potential. For this system we present results for the exchange-correlation hole and exchange-correlation energy density, and compare our findings with those from the local density approximation and generalized gradient approximation. 1. Introduction 2. The Adiabatic connection 3. Quantum Monte Carlo realization 3.1 Variational Monte Carlo 3.2 Fixed-density variance minimization 4. Cosine-wave jellium 4.1 Many-body wavefunction 5. Results and discussion 1 Introduction Density functional theory (DFT) (1, 2) is the main computational tool for the treatment of many-body effects in solid state electroni...

Maziar Nekovee, W. M. C. Foulkes, Richard J. Needs

Eugene S. Kryachko, Eduardo V. Ludeña

Sam Azadi, N. D. Drummond, Alessandro Principi +2 more

The real-space variation quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) are used to calculate the energy bands and the effective mass of the paramagnetic and ferromagnetic two-dimensional uniform electron liquid (2D-UEL). The many-body finite-size errors are minimized by performing simulations for three system sizes with the number of electrons, N = 146 , 218, and 302, for paramagnetic and N = 91 , 139, and 151 for ferromagnetic systems. We consider 2D-UEL to be within the density range 1 ≤ r s ≤ 10 . The VMC and DMC results predict that the effective mass m * of the paramagnetic 2D-UEL at high density r s = 1 is very close to 1, suggesting that the effective mass renormalization due to electron-electron interaction is negligible. We find that m * of the paramagnetic 2D-UEL obtained by the VMC and DMC methods increases by r s but with different slopes. Our VMC and DMC results for ferromagnetic 2D-UEL indicate that m * decreases rapidly by reducing the density due to the strong suppression of the electron-electron interaction.