Numerical Assessment for Accuracy and GPU Acceleration of TD-DMRG Time Evolution Schemes
Abstract
Time dependent density matrix renormalization group (TD-DMRG) has become one of the cutting edge methods of quantum dynamics for complex systems. In this paper, we comparatively study the accuracy of three time evolution schemes in TD-DMRG, the global propagation and compression method with Runge-Kutta algorithm (P&C-RK), the time dependent variational principle based methods with matrix unfolding algorithm (TDVPMU) and with projector-splitting algorithm (TDVP-PS), by performing benchmarks on the exciton dynamics of Fenna-Matthews-Olson (FMO) complex. We show that TDVP-MU and TDVP-PS yield the same result when the time step size is converged and they are more accurate than P&C-RK4, while TDVP-PS tolerates a larger time step size than TDVP-MU. We further adopt the graphical processing units (GPU) to accelerate the heavy tensor contractions in TD-DMRG and it is able to speed up the TDVP-MU and TDVP-PS schemes by up to 73 times.
Keywords
Cite
@article{arxiv.1907.12044,
title = {Numerical Assessment for Accuracy and GPU Acceleration of TD-DMRG Time Evolution Schemes},
author = {Weitang Li and Jiajun Ren and Zhigang Shuai},
journal= {arXiv preprint arXiv:1907.12044},
year = {2020}
}