Quantum Monte Carlo studies of dense hydrogen and two-dimensional Bose liquids

Abstract

Quantum Monte Carlo techniques; in their various incarnations, calculate ground state or finite temperature properties of many-body quantum systems. We apply the path-integral Monte Carlo method to hydrogen at densities and temperatures in the regime of cooperative thermal and pressure dissociation, relevant to structural models of the giant planets' interiors. We treat the protons and electrons as quantum particles, thereby avoiding the Born-Oppenheimer approximation. Fermi-Dirac exchange statistics are treated within the fixed-node approximation, with the nodes specified by the free Fermi gas. In the region of molecular dissociation, we observe properties consistent with and suggestive of a first order phase transition with positive density discontinuity $(n\sb{\rm H2}<n\sb{\rm H+H}).$ In a separate study, we apply the variational and diffusion Monte Carlo techniques to study the ground state properties of two distinct, but related, two-dimensional systems: the Bose Yukawa liquid and the Bose Coulomb liquid. The Yukawa system is a model for flux line interactions in high temperature superconductors. We determine the phase diagram as a function of mass and density and find a high density scaling relation describing the crossover to Coulomb behavior. We apply our results to a sample superconducting compound, $\rm Bi\sb2Sr\sb2CaCu\sb2O\sb8.$ Next the results of the Coulomb system are presented. We show that the predominance of long wavelength plasmons destroys Bose condensation in this system. The ground state of this system is closely related to the bosonic representation of Laughlin's wave function for the fractional quantum Hall system.