Extending the hierarchical quantum master equation approach to low temperatures and realistic band structures
arXiv:1805.10161 · doi:10.1063/1.5041716
Abstract
The hierarchical quantum master equation (HQME) approach is an accurate method to describe quantum transport in interacting nanosystems. It generalizes perturbative master equation approaches by including higher-order contributions as well as non-Markovian memory and allows for the systematic convergence to the numerically exact result. As the HQME method relies on a decomposition of the bath correlation function in terms of exponentials, however, its application to systems at low temperatures coupled to baths with complexer band structures has been a challenge. In this publication, we outline an extension of the HQME approach, which uses a re-summation over poles and can be applied to calculate transient currents at a numerical cost that is independent of temperature and band structure of the baths. We demonstrate the performance of the extended HQME approach for noninteracting tight-binding model systems of increasing complexity as well as for the spinless Anderson-Holstein model.
References in corpus (66)
- Electron transmission through molecules and molecular interfaces
- Molecular Transport Junctions: Vibrational Effects
- Phonon effects in molecular transistors: Quantum and classical treatment
- Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach
- Real-time path integral approach to nonequilibrium many-body quantum system
- Diagrammatic Monte Carlo simulation of non-equilibrium systems
- Exact quantum master equation via the calculus on path integrals
- Spin Precession and Real Time Dynamics in the Kondo Model: A Time-Dependent Numerical Renormalization-Group Study
- Quantum master equation for electron transport through quantum dots and single molecules
- Taming the dynamical sign problem in real-time evolution of quantum many-body problems
- Experimental Evidence for Quantum Interference and Vibrationally Induced Decoherence in Single-Molecule Junctions
- Resonant inelastic tunneling in molecular junctions
- Tunneling through molecules and quantum dots: master-equation approaches
- Kinetic Equations for Transport Through Single-Molecule Transistors
- Hierarchical Liouville-space approach for accurate and universal characterization of quantum impurity systems
- Time-dependent density-functional theory for open systems
- Real-time simulations of nonequilibrium transport in the single-impurity Anderson model
- Real-Time Diagrammatic Monte Carlo for Nonequilibrium Quantum Transport
- Memory Effects In Nonequilibrium Quantum Impurity Models
- Resonant Electron Transport in Single-Molecule Junctions: Vibrational Excitation, Rectification, Negative Differential Resistance and Local Cooling
- Decoherence and lead induced inter-dot coupling in nonequilibrium electron transport through interacting quantum dots: A hierarchical quantum master equation approach
- Hierarchical Quantum Master Equation Approach to Electronic-Vibrational Coupling in Nonequilibrium Transport through Nanosystems
- Tunneling through nanosystems: Combining broadening with many-particle states
- Comparative study of theoretical methods for nonequilibrium quantum transport
- The influence of ultra-fast laser pulses on electron transfer in molecular wires studied by a non-Markovian density matrix approach
- Coherent electron-phonon coupling and polaron-like transport in molecular wires
- Transient dynamics of the Anderson impurity model out of equilibrium
- Theory of Vibrationally Inelastic Electron Transport through Molecular Bridges
- Time-dependent density functional theory for quantum transport
- Phonon-mediated negative differential conductance in molecular quantum dots
- Transport in molecular states language: Generalized quantum master equation approach
- Nonequilibrium quantum systems with electron-phonon interactions: Transient dynamics and approach to steady state
- Many-body theory of electronic transport in single-molecule heterojunctions
- Quantum Interference and Decoherence in Single-Molecule Junctions: How Vibrations Induce Electrical Current
- Propagation Scheme for Non-Equilibrium Dynamics of Electron Transport in Nanoscale Devices
- Vibrational effects in laser driven molecular wires
- A Unified Stochastic Formulation of Dissipative Quantum Dynamics. I. Generalized Hierarchical Equations
- Multimode vibrational effects in single molecule conductance: A nonequilibrium Green's function approach
- Kondo memory in driven strongly-correlated quantum dots
- Transport through an Anderson impurity: Current ringing, non-linear magnetization and a direct comparison of continuous-time quantum Monte Carlo and hierarchical quantum master equations
- Path-integral simulations with fermionic and bosonic reservoirs: Transport and dissipation in molecular electronic junctions
- Iterative summation of path integrals for nonequilibrium molecular quantum transport
- A Unified Stochastic Formulation of Dissipative Quantum Dynamics. II. Beyond Linear Response of Spin Baths
- Generalized projected dynamics for non-system observables of non-equilibrium quantum impurity models
- Numerically exact, time-dependent study of correlated electron transport in model molecular junctions
- Influence of vibrational modes on the quantum transport through a nano-device
- Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems: Reservoir formulation and application to vibrational instabilities
- Dynamical symmetry breaking in transport through molecules
- Bias-Controlled Selective Excitation of Vibrational Modes in Molecular Junctions: A Route Towards Mode-Selective Chemistry
- Characterization of single-molecule pentanedithiol junctions by inelastic electron tunneling spectroscopy and first-principles calculations
- Current-induced bond rupture in single-molecule junctions
- Nonequilibrium phonon backaction on the current noise in atomic-sized junctions
- Time-Dependent Transport Through Molecular Junctions
- The formation of nonequilibrium steady states in interacting double quantum dots: When coherences dominate the charge distribution
- Vibrationally Induced Decoherence in Single-Molecule Junctions
- Effect of nonadiabatic electronic-vibrational interactions on the transport properties of single-molecule junctions
- First-principles investigation of dynamical properties of molecular devices under a steplike pulse
- Transient dynamics of a molecular quantum dot with a vibrational degree of freedom
- Sharp peaks in the conductance of double quantum dot and quantum dot spin-valve systems at high temperatures: A hierarchical quantum master equation approach
- Influence of vibrations on electron transport through nanoscale contacts
- A diagrammatic description of the equations of motion, current, and noise within the second-order von Neumann approach
- Vibrationally dependent electron-electron interactions in resonant electron transport through single-molecule junctions
- Vibrationally coupled electron transport in single-molecule junctions: The importance of electron-hole pair creation processes
- Reappearance of Kondo Effect in Serially Coupled Symmetric Triple Quantum Dots
- Hierarchical equations of motion approach to transport through an Anderson impurity coupled to interacting Luttinger liquid leads
- On the Accuracy of the Noninteracting Electron Approximation for Vibrationally Coupled Electron Transport
Cited by in corpus (29)
- Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
- Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems
- Generalization of the hierarchical equations of motion theory for efficient calculations with arbitrary correlation functions
- Removing instabilities in the hierarchical equations of motion: exact and approximate projection approaches
- Green's function methods for single molecule junctions
- Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space
- Efficient low temperature simulations for fermionic reservoirs with the hierarchical equations of motion method: Application to the Anderson impurity model
- Quantum Monte Carlo in the steady-state
- Chebyshev Hierarchical Equations of Motion for Systems with Arbitrary Spectral Densities and Temperatures
- Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. I. Formalism
- Beyond Marcus theory and the Landauer-Buttiker approach in molecular junctions. II. A self-consistent Born approach
- Revealing strong correlations in higher order transport statistics: a noncrossing approximation approach
- Hierarchical quantum master equation approach to vibronic reaction dynamics at metal surfaces
- Nonequilibrium open quantum systems with multiple bosonic and fermionic environments: A hierarchical equations of motion approach
- Lead Geometry and Transport Statistics in Molecular Junctions
- 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
- Nonequilibrium reaction rate theory: Formulation and implementation within the hierarchical equations of motion approach
- Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. II. Numerical Implementation
- Simulating Non-Markovian Quantum Dynamics on NISQ Computers Using the Hierarchical Equations of Motion
- Generalized input-output method: A new route to quantum transport junctions
- Reduced Dynamics of Full Counting Statistics
- Efficient steady state solver for the hierarchical equations of motion approach: Formulation and application to charge transport through nanosystems
- Hierarchical quantum master equation approach to charge transport in molecular junctions with time-dependent molecule-lead coupling strengths
- Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State
- Minimal pole representation for spectral functions
- Quantum entanglement and transport in non-equilibrium interacting double-dot setup: The curious role of degeneracy
- About the performance of perturbative treatments of the spin-boson dynamics within the hierarchical equations of motion approach
- Control of open quantum systems: Manipulation of a qubit coupled to a thermal bath by an external driving field