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

Suzuki’s higher order composite factorization which involves both the potential and the force is applied to imaginary time path integral simulation. The expression is more general than the original version and involves a free parameter α in the range of [0, 1]. Formal expressions are derived for statistical averages, based on both thermodynamic and quantum operator identities. 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 α is made, the higher order factorization approach is shown to be more efficient than primitive factorization by about a factor of 4 and better than other existing higher order algorithms with similar character. Actual path integral simulation tests are then made for an excess electron in supercritical helium and for bulk water, and these generally demonstrate the efficiency of the higher order factorization approach.