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arXiv · 2202.10273

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

Yaling Ke·Raffaele Borrelli·Michael Thoss
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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.

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Yaling Ke, Raffaele Borrelli, Michael Thoss. 2022-02-21. Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space. https://doi.org/10.1063/5.0088947

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