Monte Carlo studies of quantum many-body systems.

摘要

This thesis describes studies of the ground-state properties of quantum many-body systems by Monte Carlo techniques. In the first part, an algorithm is described to address the fundamental "sign problem" in quantum Monte Carlo when applied to fermion systems. Implementation of this algorithm in a parallel distributed environment is then discussed. The last part presents variational calculations of the ground states of {dollar}sp4{dollar}He clusters.; The sign problem prevents exact simulations of large many-fermion systems without uncontrolled approximations. It arises because of the antisymmetric nature of wavefunctions of fermion systems, and because of the use of random sampling. The proposed new algorithm is within the framework of the Green's function Monte Carlo method. To attack the difficulties associated with the sign problem, several new ideas are introduced to improve the Monte Carlo sampling techniques. As tests, the energies of an excited state of the He atom and of the ground states of the Li, Be, and N atoms are calculated. The algorithm remained stable and the results were in excellent agreement with the experimental values for the energies.; The fermion algorithm was parallelized and implemented on a coupled cluster of workstations using a message-passing environment. The method of parallelization maintains large granularity and therefore low overhead. Despite the stochastic nature of the algorithm, good load-balancing can be accomplished and reproducibility is ensured.; Droplets of {dollar}sp4{dollar}He atoms, as an example of simple inhomogeneous quantum many-body systems, are of interest to condensed-matter physics as well as nuclear physics. Previous variational studies of their ground states were unsatisfactory as unphysical one-body form factors had to be used to enforce a bound state. The new trial wavefunction, based on the shadow wavefunction for bulk helium, has a modified shadow-shadow correlation that reflects the varying local density in the system. A bound state is obtained without recourse to one-body form factors. The bulk wavefunction is naturally recovered as the system size is increased.