Efficient low temperature simulations for fermionic reservoirs with the hierarchical equations of motion method: Application to the Anderson impurity model

Abstract

The hierarchical equations of motion (HEOM) approach is an accurate method to simulate open system quantum dynamics, which allows for systematic convergence to numerically exact results. To represent the effects of the bath, the reservoir correlation functions are usually decomposed into the summation of multiple exponential terms in the HEOM method. Since the reservoir correlation functions become highly non-Markovian at low temperatures or when the bath has complex band structures, a present challenge is to obtain accurate exponential decompositions that allow efficient simulation with the HEOM. In this work, we employ the barycentric representation to approximate the Fermi function and hybridization functions in the frequency domain. The new method, by approximating these functions with optimized rational decomposition, greatly reduces the number of basis functions in decomposing the reservoir correlation functions, which further allows the HEOM method to be applied to ultra-low temperature and general bath structures. We demonstrate the efficiency, accuracy, and long-time stability of the new decomposition scheme by applying it to the Anderson impurity model (AIM) in the low-temperature regime with the Lorentzian and tight-binding hybridization functions.

arXiv comment43 pages, 14 figures

References in corpus (71)

• The density-matrix renormalization group
• Continuous-time Monte Carlo methods for quantum impurity models
• The numerical renormalization group method for quantum impurity systems
• Mechanical Control of Spin States in Spin-1 Molecules and the Underscreened Kondo Effect
• Phonon effects in molecular transistors: Quantum and classical treatment
• Electron transport through single Mn12 molecular magnets
• Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach
• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• The AAA algorithm for rational approximation
• Real-time path integral approach to nonequilibrium many-body quantum system
• Diagrammatic Monte Carlo simulation of non-equilibrium systems
• Energy resolution and discretization artefacts in the numerical renormalization group
• Spin Precession and Real Time Dynamics in the Kondo Model: A Time-Dependent Numerical Renormalization-Group Study
• 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
• Hierarchy of stochastic pure states for open quantum system dynamics
• NRG study of the Kondo effect in the presence of itinerant-electron ferromagnetism
• Iterative real-time path integral approach to nonequilibrium quantum transport
• Tunneling through molecules and quantum dots: master-equation approaches
• Kinetic Equations for Transport Through Single-Molecule Transistors
• Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities
• Hierarchical Liouville-space approach for accurate and universal characterization of quantum impurity systems
• Spectral functions in one-dimensional quantum systems at T>0
• Real-time simulations of nonequilibrium transport in the single-impurity Anderson model
• Real-Time Diagrammatic Monte Carlo for Nonequilibrium Quantum Transport
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Memory Effects In Nonequilibrium Quantum Impurity Models
• Numerically exact path integral simulation of nonequilibrium quantum transport and dissipation
• 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
• Time Dependent Variational Principle with Ancillary Krylov Subspace
• Nonequilibrium Dynamical Mean Field Theory: an auxiliary Quantum Master Equation approach
• A reliable Pade analytical continuation method based on a high accuracy symbolic computation algorithm
• Hierarchical Quantum Master Equation Approach to Electronic-Vibrational Coupling in Nonequilibrium Transport through Nanosystems
• Solving nonequilibrium dynamical mean-field theory using matrix product states
• Auxiliary master equation approach to non-equilibrium correlated impurities
• Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems
• Transport in molecular states language: Generalized quantum master equation approach
• Propagation Scheme for Non-Equilibrium Dynamics of Electron Transport in Nanoscale Devices
• Efficient DMFT impurity solver using real-time dynamics with Matrix Product States
• Numerically exact, time-dependent treatment of vibrationally coupled electron transport in single-molecule junctions
• Generalization of the hierarchical equations of motion theory for efficient calculations with arbitrary correlation functions
• 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
• Universal Prony fitting decomposition for optimized hierarchical quantum master equations
• Dynamics of quantum dissipation systems interacting with Fermion and Boson grand canonical bath ensembles: Hierarchical equations of motion approach
• Imaginary-time matrix product state impurity solver for dynamical mean-field theory
• Spectral functions and time evolution from the Chebyshev recursion
• 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
• Currents and Green's functions of impurities out of equilibrium -- results from inchworm Quantum Monte Carlo
• Dynamical symmetry breaking in transport through molecules
• Single-Particle Dynamics in the Vicinity of the Mott-Hubbard Metal-to-Insulator Transition
• Density-matrix renormalisation group approach to quantum impurity problems
• Dynamics of Kondo voltage splitting after a quantum quench
• Hierarchical equations of motion for impurity solver in dynamical mean-field theory
• Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space
• Hierarchical Schrödinger Equations of Motion for Open Quantum Dynamics
• Extending the hierarchical quantum master equation approach to low temperatures and realistic band structures
• Voltage quench dynamics of a Kondo system
• Chebyshev Hierarchical Equations of Motion for Systems with Arbitrary Spectral Densities and Temperatures
• Efficient mapping for Anderson impurity problems with matrix product states
• A multilayer multiconfiguration time-dependent Hartree study of the nonequilibrium Anderson impurity model at zero temperature
• Iterative path integral summation for nonequilibrium quantum transport
• Nonequilibrium reaction rate theory: Formulation and implementation within the hierarchical equations of motion approach
• Time-dependent numerical renormalization group method for multiple quenches: towards exact results for the long time limit of thermodynamic observables and spectral functions
• Quantitative comparison of Anderson impurity solvers applied to transport in quantum dots
• 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
• Absence of Coulomb Blockade in the Anderson Impurity Model at the Symmetric Point
• Entanglement entropy and computational complexity of the Anderson impurity model out of equilibrium II: driven dynamics

Cited by in corpus (18)

• Simulating Chemistry on Bosonic Quantum Devices
• Quasi-Lindblad pseudomode theory for open quantum systems
• Simulating Non-Markovian Quantum Dynamics on NISQ Computers Using the Hierarchical Equations of Motion
• 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
• Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments
• Semi-group influence matrices for non-equilibrium quantum impurity models
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Efficient Pseudomode Representation and Complexity of Quantum Impurity Models
• Nonadiabatic H-Atom Scattering Channels on Ge(111) Elucidated by the Hierarchical Equations of Motion
• About the performance of perturbative treatments of the spin-boson dynamics within the hierarchical equations of motion approach
• A Computational Framework for Simulations of Dissipative Non-Adiabatic Dynamics on Hybrid Oscillator-Qubit Quantum Devices
• Input-Output Hierarchical Equations Of Motion
• Comparison between explicit and implicit discretization strategies for a dissipative thermal environment
• Extended Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes for General Basis Functions
• Scalable tensor network algorithm for quantum impurity problems
• Exact description of fermionic reservoirs via purified damped ancillary fermions
• Making Non-Markovian master equations accessible with approximate environments