Fourth-Order Decomposition

Generalized fourth-order decompositions of imaginary time path integral: Implications of the harmonic oscillator

We develop parameterized generalized fourth-order decompositions (factorized generalized fourth-order decomposition) to replace the second-order Trotter splitting in imaginary-time path integral molecular dynamics, and optimize the parameters through analysis of the analytically solvable one-dimensional harmonic oscillator.

An efficient algorithm for the fourth-order decomposition for path integral molecular dynamics

An efficient algorithm for the fourth-order decomposition for path integral molecular dynamics.

Application of the generalized fourth-order decomposition schemes to perturbed path integral

We prove that the perturbed path integral (PPI) is at least fourth-order accurate and can be combined with generalized fourth-order decompositions to further improve the computational efficiency of PIMD by tuning the parameters.