Institut für Theoretische Physik, Johannes Kepler Universität Linz, A-4040 Linz, Austria.
J Chem Phys. 2010 Jan 28;132(4):044103. doi: 10.1063/1.3297888.
We present a new class of high-order imaginary time propagators for path integral Monte Carlo simulations that require no higher order derivatives of the potential nor explicit quadratures of Gaussian trajectories. Higher orders are achieved by an extrapolation of the primitive second-order propagator involving subtractions. By requiring all terms of the extrapolated propagator to have the same Gaussian trajectory, the subtraction only affects the potential part of the path integral. The resulting violation of positivity has surprisingly little effects on the accuracy of the algorithms at practical time steps. Thus in principle, arbitrarily high order algorithms can be devised for path integral Monte Carlo simulations. We verified the fourth, sixth, and eighth order convergences of these algorithms by solving for the ground state energy and pair distribution function of liquid (4)He, which is representative of a dense, and strongly interacting, quantum many-body system.
我们提出了一类新的用于路径积分蒙特卡罗模拟的高阶虚时间传播子，它们不需要势的更高阶导数，也不需要对高斯轨迹进行显式求积。通过对涉及减法的原始二阶传播子进行外推，可以实现更高阶。通过要求外推传播子的所有项都具有相同的高斯轨迹，减法只影响路径积分的势部分。出乎意料的是，由此产生的对正定性的违反对实际时间步长下算法的准确性几乎没有影响。因此，原则上可以为路径积分蒙特卡罗模拟设计任意高阶算法。我们通过求解液体（4）He 的基态能量和配分函数来验证这些算法的第四、第六和第八阶收敛性，液体（4）He 是一种密集且强相互作用的量子多体系统的代表。
