We propose a new framework of Hessian-free force-gradient integrators that do not require the analytical expression of the force-gradient term based on the Hessian of the potential. Due to that the new class of decomposition algorithms for separable Hamiltonian systems with quadratic kinetic energy may be particularly useful when applied to Hamiltonian systems where an evaluation of the Hessian is significantly more expensive than an evaluation of its gradient, e.g. in molecular dynamics simulations of classical systems. Numerical experiments of an N-body problem, as well as applications to the molecular dynamics step in the Hybrid Monte Carlo (HMC) algorithm for lattice simulations of the Schwinger model and Quantum Chromodynamics (QCD) verify these expectations.

翻译：本文提出了一种免Hessian力梯度积分器的新框架，该框架无需基于势能Hessian矩阵的力梯度项解析表达式。由于这类针对具有二次动能的可分离哈密顿系统的新型分解算法，在应用于Hessian计算代价显著高于梯度计算的哈密顿系统时（例如经典体系的分子动力学模拟）可能具有特殊优势。通过N体问题的数值实验，以及在施温格模型和量子色动力学晶格模拟中混合蒙特卡洛算法分子动力学步骤的应用，验证了上述预期。