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

Thesis/Dissertation · Wed Jan 01 04:00:00 EST 1992

OSTI ID:5706265

Scheinine, A L

The frustrated XY model was studied on a lattice, primarily to test 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 coupling between fermions. Finally, 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. Speedup due to Fourier acceleration was measured for frustration one-half at the transition temperature. The unfrustrated XY model was also studied. For the frustrated case, only long-distance spin correlation and the autocorrelation of the spin showed significant speedup. The frustrated case has Ising-like 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, 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 two-dimensional spinless Hubbard model with no hopping, an exact solution was found for a 4 [times] 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 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.

• Research Organization: Illinois Univ., Urbana, IL (United States)
• OSTI ID: 5706265
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
665400 -- Quantum Physics Aspects of Condensed Matter-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANGULAR MOMENTUM
CALCULATION METHODS
COUPLING
CRYSTAL MODELS
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
EQUATIONS
FERMIONS
FIELD THEORIES
FOURIER TRANSFORMATION
HUBBARD MODEL
INTEGRAL TRANSFORMATIONS
ISING MODEL
LANGEVIN EQUATION
LATTICE FIELD THEORY
MATHEMATICAL MODELS
MONTE CARLO METHOD
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
SIMULATION
SPIN
SUPERCONDUCTIVITY
THERMODYNAMIC PROPERTIES
TRANSFORMATIONS
TRANSITION TEMPERATURE