Quantum Quasi-Monte Carlo algorithm for out-of-equilibrium Green functions at long times

Abstract

We extend the recently developed Quantum Quasi-Monte Carlo (QQMC) approach to obtain the full frequency dependence of Green functions in a single calculation. QQMC is a general approach for calculating high-order perturbative expansions in power of the electron-electron interaction strength. In contrast to conventional Markov chain Monte Carlo sampling, QQMC uses low-discrepancy sequences for a more uniform sampling of the multi-dimensional integrals involved and can potentially outperform Monte Carlo by several orders of magnitudes. A core concept of QQMC is the a priori construction of a "model function" that approximates the integrand and is used to optimize the sampling distribution. In this paper, we show that the model function concept extends to a kernel approach for the computation of Green functions. We illustrate the approach on the Anderson impurity model and show that the scaling of the error with the number of integrand evaluations $N$ is $\sim 1/N^{0.86}$ in the best cases, and comparable to Monte Carlo scaling $\sim 1/N^{0.5}$ in the worst cases. We find a systematic improvement over Monte Carlo sampling by at least two orders of magnitude while using a basic form of model function. Finally, we compare QQMC results with calculations performed with the Fork Tensor Product State (FTPS) method, a recently developed tensor network approach for solving impurity problems. Applying a simple Padé approximant for the series resummation, we find that QQMC matches the FTPS results beyond the perturbative regime.

arXiv comment18 pages, 11 figures

References in corpus (33)

• The density-matrix renormalization group in the age of matrix product states
• Probing many-body dynamics on a 51-atom quantum simulator
• Kondo Physics in a Single Electron Transistor
• A Tunable Kondo Effect in Quantum Dots
• The numerical renormalization group method for quantum impurity systems
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Unifying time evolution and optimization with matrix product states
• From the Kondo Regime to the Mixed-Valence Regime in a Single-Electron Transistor
• TRIQS: A Toolbox for Research on Interacting Quantum Systems
• Dynamical density-matrix renormalization-group method
• Polaron Problem by Diagrammatic Quantum Monte Carlo
• Feynman diagrams versus Fermi-gas Feynman emulator
• Time Dependent Variational Principle with Ancillary Krylov Subspace
• Controlling Feynman diagrammatic expansions: physical nature of the pseudo gap in the two-dimensional Hubbard model
• Tunable Quantum Criticality and Super-ballistic Transport in a `Charge' Kondo Circuit
• Solving nonequilibrium dynamical mean-field theory using matrix product states
• Dynamical Mean Field Theory with the Density Matrix Renormalization Group
• Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
• Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
• Continuous Time Quantum Monte Carlo Method for Fermions: Beyond Auxiliary Field Framework
• Fork Tensor Product States - Efficient Three Orbital Real Time DMFT Solver
• Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices
• Efficient DMFT impurity solver using real-time dynamics with Matrix Product States
• Imaginary-time matrix product state impurity solver for dynamical mean-field theory
• Reconstructing non-equilibrium regimes of quantum many-body systems from the analytical structure of perturbative expansions
• Time Dependent Variational Principle for Tree Tensor Networks
• Determinant Monte Carlo for irreducible Feynman diagrams in the strongly correlated regime
• Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions
• Imaginary-time matrix product state impurity solver in a real material calculation: Spin-orbit coupling in Sr${}_2$RuO${}_4$
• A Quantum Monte Carlo algorithm for out-of-equilibrium Green's functions at long times
• The construction of good lattice rules and polynomial lattice rules
• Renormalized perturbation theory at large expansion orders
• Cancellation of vacuum diagrams and long-time limit in out-of-equilibrium diagrammatic Quantum Monte Carlo

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• Minimally Entangled Typical Thermal States Algorithms for Finite Temperature Matsubara Green Functions
• Tensor cross interpolation approach for quantum impurity problems based on the weak-coupling expansion
• Transient Dynamical Phase Diagram of the Spin-Boson Model at Finite Temperature
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