Implementation of a novel projector-splitting integrator for the multi-configurational time-dependent Hartree approach

The variational equations of motion of the multi-configuration time-dependent Hartree (MCTDH) approach contain the inverse of reduced density matrices which are typically ill-conditioned and therefore lead to small stepsizes for numerical time integration. This problem is usually dealt with via regularization of the density matrices, which works well in many cases but still calls for systematic improvement schemes. Recently this problem, its implications and possible solutions have become the subject of increased interest. Notably, a projector splitting integrator for the MCTDH approach that does not require the inversion of reduced density matrices has been proposed [C. Lubich, Appl. Math. Res. Express 2015, 311]. Here, we present the first implementation of this integration scheme. Results for low-dimensional benchmark systems are presented, and the case of initially unoccupied single-particle functions is discussed. Published by AIP Publishing.