# Large-scale quantum-dynamics with matrix product states

## TL;DR

This paper introduces a novel TD-DMRG method for simulating large-scale quantum dynamics, enabling accurate real- and imaginary-time evolution of complex molecular Hamiltonians with over 20 degrees of freedom.

## Contribution

It presents an exact, sweep-based TD-DMRG algorithm that overcomes previous scaling limitations, allowing simulation of larger and more complex quantum systems.

## Key findings

- Able to simulate systems with more than 20 degrees of freedom
- Successfully applied to excitonic and vibronic Hamiltonians
- Enables study of real- and imaginary-time quantum dynamics

## Abstract

Dynamical electronic- and vibrational-structure theories have received a growing interest in the last years due to their ability to simulate spectra recorded with ultrafast experimental techniques. The exact time evolution of a molecular system can, in principle, be obtained from the time-dependent version of full configuration interaction. Such an approach is, however, limited to few-atom systems due to the exponential increase of its cost with the system dimension. In the present work, we overcome this unfavorable scaling by employing the time-dependent density matrix renormalization group (TD-DMRG) which parametrizes the time-dependent wavefunction as a matrix product state. The time-dependent Schroedinger equation is then integrated with a sweep-based algorithm, as in standard time-independent DMRG. Unlike other TD-DMRG approaches, the one presented here leads to a set of coupled equations that can be integrated exactly. The resulting theory enables us to study real- and imaginary-time evolutions of Hamiltonians comprising more than 20 degrees of freedom that are challenging for current state-of-the-art quantum dynamics algorithms. We apply our algorithm to the simulation of quantum dynamics of models of increasing complexity, ranging from simple excitonic Hamiltonians to more complex ab-initio vibronic ones.