An efficient method for quantum impurity problems out of equilibrium

Abstract

We introduce an efficient method to simulate dynamics of an interacting quantum impurity coupled to non-interacting fermionic reservoirs. Viewing the impurity as an open quantum system, we describe the reservoirs by their Feynman-Vernon influence functionals (IF). The IF are represented as matrix-product states in the temporal domain, which enables an efficient computation of dynamics for arbitrary interactions. We apply our method to study quantum quenches and transport in an Anderson impurity model, including highly non-equilibrium setups, and find favorable performance compared to state-of-the-art methods. The computational resources required for an accurate computation of dynamics scale polynomially with evolution time, indicating that a broad class of out-of-equilibrium quantum impurity problems are efficiently solvable. This approach will provide new insights into dynamical properties of mesoscopic devices and correlated materials.

arXiv comment11 pages, 6 figures

References in corpus (53)

• Many-Body Physics with Ultracold Gases
• Nonequilibrium dynamical mean-field theory and its applications
• Time-evolution methods for matrix-product states
• Efficient simulation of strong system-environment interactions
• 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
• Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
• Real-time path integral approach to nonequilibrium many-body quantum system
• Diagrammatic Monte Carlo simulation of non-equilibrium systems
• Kondo effect in quantum dots
• A non-Markovian decoherence theory for double dot charge qubit
• Taming the dynamical sign problem in real-time evolution of quantum many-body problems
• Exact dynamics in dual-unitary quantum circuits
• Iterative real-time path integral approach to nonequilibrium quantum transport
• Matrix Product States for dynamical simulation of infinite chains
• Real-Time Diagrammatic Monte Carlo for Nonequilibrium Quantum Transport
• Memory Effects In Nonequilibrium Quantum Impurity Models
• Numerically exact path integral simulation of nonequilibrium quantum transport and dissipation
• Numerically Exact Long Time Magnetization Dynamics at the Nonequilibrium Kondo Crossover of the Anderson Impurity Model
• Localized magnetic moments with tunable spin exchange in a gas of ultracold fermions
• Weak-coupling quantum Monte Carlo calculations on the Keldysh contour: theory and application to the current-voltage characteristics of the Anderson model
• Solving nonequilibrium dynamical mean-field theory using matrix product states
• Transient dynamics of the Anderson impurity model out of equilibrium
• Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
• Variational Study of Fermionic and Bosonic Systems with Non-Gaussian States: Theory and Applications
• Auxiliary master equation approach to non-equilibrium correlated impurities
• A nonequilibrium theory for transient transport dynamics in nanostructures via the Feynman-Vernon influence functional approach
• Influence matrix approach to many-body Floquet dynamics
• Complexity of quantum impurity problems
• Nonequilibrium Steady-State Transport in Quantum Impurity Models: a Thermofield and Quantum Quench Approach using Matrix Product States
• Compression of Correlation Matrices and an Efficient Method for Forming Matrix Product States of Fermionic Gaussian States
• Numerically Exact Long Time Behavior of Nonequilibrium Quantum Impurity Models
• Temporal entanglement, quasiparticles and the role of interactions
• Reconstructing non-equilibrium regimes of quantum many-body systems from the analytical structure of perturbative expansions
• Exploring the Kondo model in and out of equilibrium with alkaline-earth atoms
• Real time evolution of Anderson impurity models via tensor network influence functionals
• Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain
• Solving quantum impurity problems in and out of equilibrium with variational approach
• Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions
• Constructing Tensor Network Influence Functionals for General Quantum Dynamics
• Efficient simulation of open quantum systems coupled to a fermionic bath
• Nonequilibrium, spatio-temporal formation of the Kondo screening-cloud on a lattice
• Spatiotemporal buildup of the Kondo screening cloud
• Scaling of temporal entanglement in proximity to integrability
• Renormalized Lindblad Driving: A Numerically-Exact Nonequilibrium Quantum Impurity Solver
• Time evolution of the Kondo resonance in response to a quench
• Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality
• Open System Tensor Networks and Kramers' Crossover for Quantum Transport
• Light cone tensor network and time evolution
• Matrix product state algorithms for Gaussian fermionic states
• Few-body nature of Kondo correlated ground states
• Nonequilibrium Kondo effect in a magnetic field: Auxiliary master equation approach
• Long-time dynamics of quantum chains: transfer-matrix renormalization group and entanglement of the maximal eigenvector

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