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

• URL: http://arxiv.org/abs/2202.10273v1
• Date: Mon, 21 Feb 2022 14:39:23 GMT
• Title: Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space
• Authors: Yaling Ke, Raffaele Borrelli, Michael Thoss
• Abstract summary: We extend the twin-space formulation of the hierarchical equations of motion approach to nonequilibrium scenarios. The new approach facilitates accurate simulations of non-equilibrium quantum dynamics in larger and more complex open quantum systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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