Comparative Study of Numerical Techniques for the Simulation of the 1-D Spinless Fermion Model.

G.M. Buend�a

A comparative study of the efficiency of different algorithms (Metropolis, Langevin, and Hybrid) for the simulation of a one-dimensional spinless fermion model with a half-filled band is presented. The Metropolis updating of the fields is performed with an algorithm introduced by Blankenbecler, Scalapino, and Sugar. The density-density correlation function, the order parameter, and the autocorrelation are calculated. A study of the dependence of the systematic errors on the temperature and the step size for the Langevin and hybrid algorithms is presented. The relation between the accuracy and the speed of the algorithms is studied.

Alan L. Scheinine

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.

Richard T. Scalettar

Matteo Beccaria A

We present an improved upper bound for the ground-state energy of lattice fermion models with a sign problem. The bound can be computed by numerical simulation of a recently proposed family of deformed Hamiltonians with no sign problem. For one-dimensional models, we expect the bound to be particularly effective and practical extrapolation procedures are discussed. In particular, in a model of spinless interacting fermions and in the Hubbard model at various filling and Coulomb repulsion we show how such techniques can estimate the ground-state energies and correlation function with great accuracy.

T. Cheng, E.R. Gospodarczyk, Qichang C. Su +1 more