On processed splitting methods and high-order actions in path-integral Monte Carlo simulations.
Processed splitting methods are particularly well adapted to carry out path-integral Monte Carlo (PIMC) simulations: since one is mainly interested in estimating traces of operators, only the kernel of the method is necessary to approximate the thermal density matrix. Unfortunately, they suffer the same drawback as standard, nonprocessed integrators: kernels of effective order greater than two necessarily involve some negative coefficients. This problem can be circumvented, however, by incorporating modified potentials into the composition, thus rendering schemes of higher effective order. In this work we analyze a family of fourth-order schemes recently proposed in the PIMC setting, paying special attention to their linear stability properties, and justify their observed behavior in practice. We also propose a new fourth-order scheme requiring the same computational cost but with an enlarged stability interval.
Departament de Matemàtiques and Institut de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, E-12071 Castellón, Spain. fernando.casas@uji.es
Fernando
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Casas