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

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 Schrödinger-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.

12 pages, 4 figures

References in corpus (26)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Molecular Transport Junctions: Vibrational Effects
• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• From density-matrix renormalization group to matrix product states
• Circuit Quantum Electrodynamics with a Spin Qubit
• Multilayer multi-configuration time-dependent Hartree method: implementation and applications to a Henon-Heiles Hamiltonian and to pyrazine
• Real-time path integral approach to nonequilibrium many-body quantum system
• Diagrammatic Monte Carlo simulation of non-equilibrium systems
• Spin Precession and Real Time Dynamics in the Kondo Model: A Time-Dependent Numerical Renormalization-Group Study
• Tunneling through molecules and quantum dots: master-equation approaches
• Hierarchical Liouville-space approach for accurate and universal characterization of quantum impurity systems
• Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach
• Time evolution algorithms for Matrix Product States and DMRG
• Time Dependent Variational Principle with Ancillary Krylov Subspace
• Hierarchical Quantum Master Equation Approach to Electronic-Vibrational Coupling in Nonequilibrium Transport through Nanosystems
• Current-induced atomic dynamics, instabilities, and Raman signals: Quasi-classical Langevin equation approach
• Removing instabilities in the hierarchical equations of motion: exact and approximate projection approaches
• Dynamic Coulomb blockade in single-lead quantum dots
• Constructing Tensor Network Influence Functionals for General Quantum Dynamics
• Many-body quantum state diffusion for non-Markovian dynamics in strongly interacting systems
• Non-Markovian Stochastic Schrödinger Equation: Matrix Product State Approach to the Hierarchy of Pure States
• Nonequilibrium open quantum systems with multiple bosonic and fermionic environments: A hierarchical equations of motion approach
• Current-induced dissociation in molecular junctions beyond the paradigm of vibrational heating: The role of anti-bonding electronic states
• Unraveling current-induced dissociation mechanisms in single-molecule junctions

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• Towards Quantum Simulation of Non-Markovian Open Quantum Dynamics: A Universal and Compact Theory
• A pseudo-fermion method for the exact description of fermionic environments: from single-molecule electronics to Kondo resonance
• Nonequilibrium reaction rate theory: Formulation and implementation within the hierarchical equations of motion approach
• A simple improved low temperature correction for the hierarchical equations of motion
• Simulating Non-Markovian Quantum Dynamics on NISQ Computers Using the Hierarchical Equations of Motion
• Coupled charge and energy transfer dynamics in light harvesting complexes from a hybrid hierarchical equations of motion approach
• Managing Temperature in Open Quantum Systems Strongly Coupled with Structured Environments
• Current-induced bond rupture in single-molecule junctions: Effects of multiple electronic states and vibrational modes
• Effective Modeling of Open Quantum Systems by Low-rank Discretization of Structured Environments
• Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments
• Nonadiabatic H-Atom Scattering Channels on Ge(111) Elucidated by the Hierarchical Equations of Motion
• A Computational Framework for Simulations of Dissipative Non-Adiabatic Dynamics on Hybrid Oscillator-Qubit Quantum Devices
• About the performance of perturbative treatments of the spin-boson dynamics within the hierarchical equations of motion approach
• Input-Output Hierarchical Equations Of Motion
• Numerically exact quantum dynamics with tensor networks: Predicting the decoherence of interacting spin systems
• Markovian Embeddings of Non-Markovian Open System Dynamics