Fourier-accelerated Langevin simulation of the frustrated XY model and simulation of the spinless and spin one-half Hubbard model

The frustrated XY model was studied on a lattice, primarily to test the Fourier transform acceleration technique for a phase transition having more field structure than just spinwaves and vortices. Also, the spinless Hubbard model without hopping was simulated using continuous variables for the auxiliary field that mediates the coupling between fermions. Finally, the spin one-half Hubbard model was studied with a technique that sampled the fermion occupation configurations. The frustrated two-dimensional XY model was simulated using the Langevin equation with Fourier transform acceleration. The speedup due to Fourier acceleration was measured for frustration one-half at the transition temperature. For comparison, the unfrustrated XY model was also studied. For the frustrated case, only the long-distance spin correlation and the autocorrelation of the spin showed significant speedup. The frustrated case has Isinglike domains. It was found that Fourier acceleration speeds the evolution of spinwaves but has negligible effect on the Ising-like domains. In the Hubbard model, the fermion determinant weight factor in the partition function changes sign, causing large statistical fluctuations of observables. A technique was found for sampling configuration space using continuous auxiliary fields, despite energy barriers where the fermion determinant changes sign. For the two-dimensional spinless Hubbard model with no hopping, an exact solution was found for a 4 x 4 lattice; which could be compared to numerical simulations. The sign problem remained, and was found to be related to the sign problem encountered when a discrete variable is used for the auxiliary field. For the spin one-half Hubbard model, a Monte Carlo simulation was done in which the fermion occupation configurations were varied. Rather than integrate-out the fermions and make a numerical estimate of the sum over the auxiliary field, the auxiliary field was integrated-out and a numerical estimate was made of the sum over fermion configurations.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2011

Author dc:creator

• Scheinine, Alan Louis

Contributors dc:contributor

• Kogut, John B.

• frustrated XY model
• Fourier-accelerated Langevin simulation
• Hubbard model
• computational physics

Statement dc:rights

• 1992 Alan Louis Scheinine

Language dc:language

en

Identifier

3488516

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/18883