Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space

TL;DR

This paper introduces an advanced tensor network method combining hierarchical equations of motion and matrix product states to simulate complex non-equilibrium quantum dynamics in hybrid fermionic and bosonic environments, enabling larger system analysis.

Contribution

It extends the twin-space hierarchical equations of motion with matrix product states to handle hybrid environments in non-equilibrium quantum systems.

Findings

Accurately simulates non-equilibrium dynamics in larger systems.

Demonstrates effectiveness on a molecular junction model.

Enables detailed study of current-induced vibrational excitation.

Abstract

We extend the twin-space formulation of the hierarchical equations of motion approach in combination with the matrix product state representation (introduced in J. Chem. Phys. 150, 234102, [2019]) to nonequilibrium scenarios where the open quantum system is coupled to a hybrid fermionic and bosonic environment. The key ideas used in the extension are a reformulation of the hierarchical equations of motion for the auxiliary density matrices into a time-dependent Schr\"odinger-like equation for an augmented multi-dimensional wave function as well as a tensor decomposition into a product of low-rank matrices. The new approach facilitates accurate simulations of non-equilibrium quantum dynamics in larger and more complex open quantum systems. The performance of the method is demonstrated for a model of a molecular junction exhibiting current-induced mode-selective vibrational excitation.