Hierarchical Liouville-space approach for accurate and universal characterization of quantum impurity systems

Abstract

A hierarchical equations of motion (HEOM) based numerical approach is developed for accurate and efficient evaluation of dynamical observables of strongly correlated quantum impurity systems. This approach is capable of describing quantitatively Kondo resonance and Fermi liquid characteristics, achieving the accuracy of latest high-level numerical renormalization group approach, as demonstrated on single-impurity Anderson model systems. Its application to a two-impurity Anderson model results in differential conductance versus external bias, which correctly reproduces the continuous transition from Kondo states of individual impurity to singlet spin-states formed between two impurities. The outstanding performance on characterizing both equilibrium and nonequilibrium properties of quantum impurity systems makes the HEOM approach potentially useful for addressing strongly correlated lattice systems in the frame work of dynamical mean field theory.

5 pages, 4 figures, to appear in PRL

References in corpus (18)

• Angle-resolved photoemission spectroscopy of the cuprate superconductors
• Correlated Electrons in High Temperature Superconductors
• Efficient classical simulation of slightly entangled quantum computations
• Continuous-time Monte Carlo methods for quantum impurity models
• The numerical renormalization group method for quantum impurity systems
• Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Numerical Renormalization Group Calculations for the Self-energy of the impurity Anderson model
• Conformal Field Theory Approach to the 2-Impurity Kondo Problem: Comparison with Numerical Renormalization Group Results
• Conserving GW scheme for nonequilibrium quantum transport in molecular contacts
• Transition between Quantum States in a Parallel-Coupled Double-Quantum-Dot
• Dynamical Coulomb Blockade and the Derivative Discontinuity of Time-Dependent Density Functional Theory
• Correlation Induced Insulator to Metal Transitions
• Equation of motion approach to the solution of Anderson model
• Dynamic Coulomb blockade in single-lead quantum dots
• Correlation effects in bistability at the nanoscale: steady state and beyond
• On the scaling spectrum of the Anderson impurity model
• Spectral function of the Anderson impurity model at finite temperatures

Cited by in corpus (75)

• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• 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
• Green's functions from real-time bold-line Monte Carlo: spectral properties of the nonequilibrium Anderson impurity model
• QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics
• Kondo memory in driven strongly-correlated quantum dots
• Exact open quantum system dynamics using the Hierarchy of Pure States (HOPS)
• Green's function methods for single molecule junctions
• Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems: Reservoir formulation and application to vibrational instabilities
• Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation
• Real time evolution of Anderson impurity models via tensor network influence functionals
• 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
• Local temperatures of strongly-correlated quantum dots out of equilibrium
• Current-induced bond rupture in single-molecule junctions
• Extending the hierarchical quantum master equation approach to low temperatures and realistic band structures
• Efficient low temperature simulations for fermionic reservoirs with the hierarchical equations of motion method: Application to the Anderson impurity model
• Stochastic Representation of Non-Markovian Fermionic Quantum Dissipation
• Quantum mechanics of open systems: Dissipaton theories
• Non-Markovian Quantum Exceptional Points
• Time-Dependent Transport Through Quantum-Impurity Systems with Kondo Resonance
• Hierarchical quantum master equation approach to current fluctuations in nonequilibrium charge transport through nanosystems
• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. I. Formalism
• Time-dependent density-functional theory for real-time electronic dynamics on material surfaces
• Continuous Measurement of a Non-Markovian Open Quantum System
• 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
• The Fermionic influence superoperator: a canonical derivation for the development of methods to simulate the influence of a Fermionic environment on a quantum system with arbitrary parity symmetry
• A pseudo-fermion method for the exact description of fermionic environments: from single-molecule electronics to Kondo resonance
• Long-range Exchange Interaction in Triple Quantum Dots in the Kondo Regime
• HierarchicalEOM.jl: An efficient Julia framework for hierarchical equations of motion in open quantum systems
• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. II. Numerical Implementation
• The thermodynamic meaning of local temperature of nonequilibrium open quantum systems
• Generalized input-output method: A new route to quantum transport junctions
• QuantumToolbox.jl: An efficient Julia framework for simulating open quantum systems
• Projective Truncation Approximation for Equations of Motion of Two-Time Green's Functions
• Reduced Dynamics of Full Counting Statistics
• Reappearance of Kondo Effect in Serially Coupled Symmetric Triple Quantum Dots
• Kondo QED: The Kondo effect and photon trapping in a two-impurity Anderson model ultra-strongly coupled to light
• Extended dissipaton equation of motion for electronic open quantum systems: Application to the Kondo impurity model
• Non-Markovian skin effect
• Efficient steady state solver for the hierarchical equations of motion approach: Formulation and application to charge transport through nanosystems
• Nonequilibirum noise spectrum and Coulomb-blockade-assisted Rabi interference in a double-dot Aharonov-Bohm interferometer
• Time-dependent quantum transport through an interacting quantum dot beyond sequential tunneling: second-order quantum rate equations
• Vertex corrections to conductivity in the Holstein model: A numerical-analytical study
• Theoretical formulations on thermodynamics of quantum impurity systems
• Hierarchical quantum master equation approach to charge transport in molecular junctions with time-dependent molecule-lead coupling strengths
• Charge transport limited by nonlocal electron-phonon interaction. II. Numerically exact quantum dynamics in the slow-phonon regime
• Charge transport limited by nonlocal electron-phonon interaction. I. Hierarchical equations of motion approach
• Manipulating quantum coherence of charge states in interacting double-dot Aharonov-Bohm interferometers
• Mechanism of current noise spectrum in a nonequilibirum Kondo dot system
• Correlated vibration-solvent and Duschinsky effects on electron transfer dynamics and optical spectroscopy
• Effect of quantum resonances on local temperature in nonequilibrium open systems
• Memory effect preserved time-local approach to noise spectrum of transport current
• Bias-induced chiral current and topological blockadein triple quantum dots
• The Anderson impurity model out of equilibrium: Assessing the accuracy of simulation techniques with an exact current-occupation relation
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Precise simulation for single-hole spin control in semiconductor quantum dots
• Performance of the T-matrix based master equation for Coulomb drag in double quantum dots
• Natural Orbital-Based Lanczos Method for Anderson Impurity Models
• A Standard Basis Operator Equation of Motion Impurity Solver for Dynamical Mean Field Theory
• The mixing of polarizations in the acoustic excitations of disordered media with local isotropy
• Input-Output Hierarchical Equations Of Motion
• Phase-controlled quantum transport signatures in a quantum dot-Majorana hybrid ring system
• Number-resolved master equation approach to quantum transport under the self-consistent Born approximation
• Rayleigh anomalies and disorder-induced mixing of polarizations at nanoscale in amorphous solids. Testing 1-octyl-3-methylimidazolium chloride glass
• Long-range Entanglement of Kondo Clouds in Open Triple Quantum Dots
• Nonequilibrium shot noise spectrum through a quantum dot in the Kondo regime: A master equation approach under self-consistent Born approximation
• Dynamic Transport Characteristics of Side-Coupled Double Quantum-Impurity Systems
• Improved strong-coupling perturbation theory of the symmetric Anderson impurity model
• Thermopower of few-electron quantum dots with Kondo correlations
• Purified pseudomode model for nonlinear system-bath interactions
• Spectral Functions of the Holstein Polaron: Exact and Approximate Solutions
• Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice
• Exact description of fermionic reservoirs via purified damped ancillary fermions