LOW-TEMPERATURE VARIATIONAL APPROXIMATION FOR THE FEYNMAN QUANTUM PROPAGATOR AND ITS APPLICATION TO THE SIMULATION OF QUANTUM-SYSTEMS

The low-temperature propagator of Mak and Andersen [J. Chem. Phys. 92, 2953 (1990)] allows for much more rapid convergence of Feynman path integral computer simulations of quantum systems. The effectiveness of this propagator is very sensitive to the choice of an effective frequency and the choice of this made by Mak and Andersen, although good, is not optimum. In this paper a harmonic reference system is used together with a variation principle to compute this effective frequency. Simulations show that when this is used in the low temperature propagator, the results converge much more rapidly than for other choices of the frequency. Moreover, an energy estimator is derived, which allows this effective potential to be used for the determination of the energy of the quantum system. In addition, using a cumulant expansion of the centroid density in the free particle reference system, an effective potential along with a corresponding energy estimator is derived and compared to the above. © 1990 American Institute of Physics.