Inchworm Monte Carlo for exact non-adiabatic dynamics I. Theory and algorithms
arXiv:1610.09566 · doi:10.1063/1.4974328
Abstract
In this paper we provide a detailed description of the inchworm Monte Carlo formalism for the exact study of real-time non-adiabatic dynamics. This method optimally recycles Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. Using the example of the spin-boson model, we formulate the inchworm expansion in two distinct ways: The first with respect to an expansion in the system-bath coupling and the second as an expansion in the diabatic coupling. The latter approach motivates the development of a cumulant version of the inchworm Monte Carlo method, which has the benefit of improved scaling. This paper deals completely with methodology, while Paper II provides a comprehensive comparison of the performance of the inchworm Monte Carlo algorithms to other exact methodologies as well as a discussion of the relative advantages and disadvantages of each.
arXiv comment16 pages, 6 figures
References in corpus (34)
- Many-Body Physics with Ultracold Gases
- Continuous-time Monte Carlo methods for quantum impurity models
- Quantum Cluster Theories
- Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
- A continuous-time solver for quantum impurity models
- Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
- Continuum variational and diffusion quantum Monte Carlo calculations
- Worm algorithms for classical statistical models
- Real-time path integral approach to nonequilibrium many-body quantum system
- Diagrammatic Monte Carlo simulation of non-equilibrium systems
- Continuous-time auxiliary field Monte Carlo for quantum impurity models
- Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity
- Taming the dynamical sign problem in real-time evolution of quantum many-body problems
- Suppression of the critical temperature for superfluidity near the Mott transition: validating a quantum simulator
- Low-temperature dynamical simulation of spin-boson systems
- Efficient DMFT-simulation of the Holstein-Hubbard Model
- Memory Effects In Nonequilibrium Quantum Impurity Models
- Revealing Superfluid--Mott-Insulator Transition in an Optical Lattice
- Numerically Exact Long Time Magnetization Dynamics at the Nonequilibrium Kondo Crossover of the Anderson Impurity Model
- Dynamical Screening in Correlated Electron Materials
- Green's functions from real-time bold-line Monte Carlo: spectral properties of the nonequilibrium Anderson impurity model
- Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices
- Bold Line Diagrammatic Monte Carlo Method: General formulation and application to expansion around the Non-Crossing Approximation
- Green's functions from real-time bold-line Monte Carlo
- Crossover from nonadiabatic to adiabatic electron transfer reactions: Multilevel blocking Monte Carlo simulations
- Real-Time Dynamics in Quantum Impurity Models with Diagrammatic Monte Carlo
- Path-integral Monte Carlo Simulations without the Sign Problem: Multilevel Blocking Approach for Effective Actions
- Inchworm Monte Carlo for exact non-adiabatic dynamics II. Benchmarks and comparison with established methods
- Generalized projected dynamics for non-system observables of non-equilibrium quantum impurity models
- Phonon-enhanced relaxation and excitation in the Holstein-Hubbard model
- The Anderson--Holstein Model in Two Flavors of the Non--Crossing Approximation
- Voltage quench dynamics of a Kondo system
- Cumulant Expansions and the Spin-Boson Problem
- A discrete Hubbard-Stratonovich decomposition for general, fermionic two-body interactions
Cited by in corpus (50)
- Exploiting the causal tensor network structure of quantum processes to efficiently simulate non-Markovian path integrals
- Inchworm Monte Carlo for exact non-adiabatic dynamics II. Benchmarks and comparison with established methods
- Numerically exact full counting statistics of the nonequilibrium Anderson impurity model
- Green's function methods for single molecule junctions
- Reconstructing non-equilibrium regimes of quantum many-body systems from the analytical structure of perturbative expansions
- Linear and nonlinear spectroscopy from quantum master equations
- Constructing Tensor Network Influence Functionals for General Quantum Dynamics
- Dynamics of Kondo voltage splitting after a quantum quench
- Ehrenfest+R Dynamics I: A Mixed Quantum-Classical Electrodynamics Simulation of Spontaneous Emission
- A Quantum Monte Carlo algorithm for out-of-equilibrium Green's functions at long times
- Quantum Monte Carlo in the steady-state
- Quantum Monte Carlo solution of the dynamical mean field equations in real time
- Inclusion-Exclusion Principle for Many-Body Diagrammatics
- Multiorbital Quantum Impurity Solver for General Interactions and Hybridizations
- Numerically exact counting statistics of energy current in the Kondo regime
- Analog Quantum Simulation of the Dynamics of Open Quantum Systems with Quantum Dots and Microelectronic Circuits
- Revealing strong correlations in higher order transport statistics: a noncrossing approximation approach
- Lead Geometry and Transport Statistics in Molecular Junctions
- Quantum Impurity Models coupled to Markovian and Non Markovian Baths
- : Implementation of the Stochastic Optimization Method for Analytic Continuation
- Photo-induced nonequilibrium states in Mott insulators
- A discrete memory-kernel for multi-time correlations in non-Markovian quantum processes
- Inclusion-Exclusion Principle for Open Quantum Systems with Bosonic Bath
- Cancellation of vacuum diagrams and long-time limit in out-of-equilibrium diagrammatic Quantum Monte Carlo
- Resolving the nonequilibrium Kondo singlet in energy- and position-space using quantum measurements
- Compact and complete description of non-Markovian dynamics
- Mean Field Theory of Thermal Energy Transport in Molecular Junctions
- On the sampling complexity of open quantum systems
- Extended dissipaton equation of motion for electronic open quantum systems: Application to the Kondo impurity model
- Solving quantum impurity problems on the L-shaped Kadanoff-Baym contour
- The Bold-Thin-Bold Diagrammatic Monte Carlo Method for Open Quantum Systems
- Effective low-energy models for superconducting impurity systems
- Tree-based Implementation of the Small Matrix Path Integral for System-Bath Dynamics
- Stark-Many body localization in interacting infinite dimensional systems
- Differential Equation Based Path Integral for System-Bath Dynamics
- Real-Time Simulation of Open Quantum Spin Chains with Inchworm Method
- Exact real-time dynamics of single-impurity Anderson model from a single-spin hybridization-expansion
- Transient dynamical phase diagram of the spin-boson model
- Capturing long-range memory structures with tree-geometry process tensors
- Non-Markovian dynamics of a two-level system in a bosonic bath and a Gaussian fluctuating environment with finite correlation time
- Dressed Quantum Trajectories: Novel Approach to the non-Markovian Dynamics of Open Quantum Systems on a Wide Time Scale
- Information Loss Pathways in a Numerically Exact Simulation of a non-Markovian Open Quantum System
- Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian Approximation
- Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm
- Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
- Simulation of Spin Chains with off-diagonal Coupling Using Inchworm Method
- Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench
- Separation of relaxation timescales via strong system-bath coupling: Dissipative three-level system as a case study
- Transient Dynamical Phase Diagram of the Spin-Boson Model at Finite Temperature
- Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model