Spin Polarization of Ground State Electron Gas at Low Densities

The electron gas is of great interest in condensed matter physics. It is a simple yet intriguing model that exhibits rich results that help our understanding of the electronic structure of materials. In this work we use Quantum Monte Carlo simulations to study the spontaneous polarization of electron gas at low densities, for both two and three dimensions. Quantum Monte Carlo is a powerful method to tackle many-body Fermion problems, and its high accuracy has been demonstrated in many previous calculations. The methods we use include variational Monte Carlo and mixed-phase pure diffusion Monte Carlo methods. To construct a high quality wavefunction or density matrix at zero and finite temperature, we apply the Variational Density Matrix method. We use Random Phase Approximation to derive two-body Jastrow correlation functions. We also include backflow and threebody correlations in the wavefunction, to get a better upper bound for the ground state energies at both variational and fixed-phase level. In order to reduce the finite size effect at small system sizes, we apply Twist Averaged Boundary Conditions on electron gas. To our knowledge, this is the first application on continuum systems. With the above methods, we first calculate ground state energies of electron gas at the variational level. Our study shows that the finite size efect is significantly reduced with Twist Averaged Boundary Conditions compared to Periodic Boundary Conditions. To get a better upper bound in ground state energies, we also perform fixed-phase pure diffusion Monte Carlo calculations on electron gas. With the fixed-phase restriction, an efective potential term comes into the Hamiltonian. We present a cubic polynomial interpolation for an accurate estimation of the path integral of this potential. We perform our calculations with different densities and polarizations, to determine the polarization transition point of ground state electron gas in both two and three dimensions.U of I Onlythesis/dissertatio