# A Further Comparison of MPS and TTNS for Nonadiabatic Dynamics of Exciton Dissociation

## TL;DR

This study systematically compares MPS and TTNS tensor network methods for simulating exciton dissociation, demonstrating that increasing bond dimensions ensures both methods converge to accurate solutions, thus validating their reliability.

## Contribution

It provides a comprehensive comparison of MPS and TTNS, highlighting the importance of bond dimension scaling for accurate quantum dynamics simulations.

## Key findings

- Discrepancies in previous results are mainly due to insufficient bond dimensions.
- Increasing bond dimensions reduces differences in electronic state occupancy to below 10%.
- Optimized TTNS structures further improve accuracy and efficiency.

## Abstract

Tensor networks, such as matrix product states (MPS) and tree tensor network states (TTNS), are powerful ans\"atze for simulating quantum dynamics. While both ans\"atze are theoretically exact in the limit of large bond dimensions, [J. Chem. Theory Comput. 2024, 20, 8767-8781] reported a non-negligible discrepancy in its calculations for exciton dissociation. To resolve this inconsistency, we conduct a systematic comparison using Renormalizer, a unified software framework for MPS and TTNS. By revisiting the benchmark P3HT:PCBM heterojunction model, we show that the observed discrepancies arise primarily from insufficient bond dimensions. By increasing bond dimensions, we reduce the relative difference in occupancy for weakly populated electronic states from up to 60% towards the end of the simulation to less than 10% and the absolute difference from 0.05 to 0.005. We also discuss the impact of tensor network structures on accuracy and efficiency, with the difference further reduced by an optimized TTNS structure. Our results confirm that both methods converge to numerically exact solutions when bond dimensions are adequately scaled. This work not only validates the reliability of both methods but also provides high-accuracy benchmark data for future developments in quantum dynamics simulations.