Applications of higher order composite factorization schemes in imaginary time path integral simulations

Suzuki's higher order composite factorization which involves both the poten tial and the force is applied to imaginary time path integral simulation. T he expression is more general than the original version and involves a free parameter alpha in the range of [0, 1]. Formal expressions are derived for statistical averages, based on both thermodynamic and quantum operator ide ntities. The derived expressions are then tested for one-dimensional model systems using the numerical matrix multiplication method, which involves no statistical error. When an optimum choice of alpha is made, the higher ord er factorization approach is shown to be more efficient than primitive fact orization by about a factor of 4 and better than other existing higher orde r algorithms with similar character. Actual path integral simulation tests are then made for an excess electron in supercritical helium and for bulk w ater, and these generally demonstrate the efficiency of the higher order fa ctorization approach. (C) 2001 American Institute of Physics.