Fourier-accelerated Langevin simulation of the frustrated XY model and simulation of the spinless and spin one-half Hubbard model
Scheinine, Alan Louis
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https://hdl.handle.net/2142/18883
Description
Title
Fourier-accelerated Langevin simulation of the frustrated XY model and simulation of the spinless and spin one-half Hubbard model
Author(s)
Scheinine, Alan Louis
Issue Date
1992
Doctoral Committee Chair(s)
Kogut, John B.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
frustrated XY model
Fourier-accelerated Langevin simulation
Hubbard model
computational physics
Language
en
Abstract
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.
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