Quantum Monte Carlo Studies of Ultra-cold Molecules and Rashba Interactions.

摘要

Quantum Monte Carlo method(QMC) has proved to be powerful in predicting material properties. We have applied QMC method to solve different electronic structure problems including ultra-cold molecules, molecules with heavy elements and electron gas with presence of spin-orbit interaction.;The ultracold molecules are of great interest to experiments. Two kinds of ultracold molecules: LiSr and KRb, are studied in this thesis. Both binding energy curve and dipole moment curve are calculated as a function of bond length. We use Hartree Fock(HF), Configuration Interaction(CI) and the Quantum Monte Carlo methods and compare all the results. We assess the many-body effects on the calculated quantities and the calculation shows the dipole moment is quite sensitive to the treatment of correlation.;The dissociation energy of Thorium halide molecules(ThCln and ThBrn) is studied using QMC and the behaviour of the molecules with different number of halides is analyzed. We also compare our results with density functional theory calculations and experimental data. The comparison shows a reasonable agreement for ThCln case, however, ThBr n case remains problematic.;Furthermore, we carry out a development of a new quantum Monte Carlo method for calculations with Hamiltonians that contain spin-dependent operators. This is crucial in particular for treatment of spin-orbit effects in systems with heavy atoms or effective spin-orbit couplings such as the Rashba interaction. We introduce a continuous spin representation and develop a new spin-sampling procedure in which the spin becomes a dynamic variable instead of being restricted to a static label. Due to the presence of the spin-orbit term in the Hamiltonian, the wavefunction becomes complex. For the purpose of the treatment of complex wavefunctions, fixed-phase approximation is applied. The energies of electron gas with Rashba interactions are calculated at different densities. The result is very promising and comparable to other independent calculations in the literature.