# Numerical Assessment for Accuracy and GPU Acceleration of TD-DMRG Time Evolution Schemes

## TL;DR

This paper evaluates the accuracy of three TD-DMRG time evolution schemes and demonstrates significant GPU acceleration, enhancing the efficiency of quantum dynamics simulations for complex systems.

## Contribution

It provides a comparative analysis of three TD-DMRG schemes and introduces GPU acceleration to significantly speed up tensor contractions in these methods.

## Key findings

- TDVP-PS allows larger time steps than TDVP-MU.
- TDVP-MU and TDVP-PS are more accurate than P&C-RK4.
- GPU acceleration speeds up TDVP schemes by up to 73 times.

## 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.