Inchworm quasi Monte Carlo for quantum impurities

Abstract

The inchworm expansion is a promising approach to solving strongly correlated quantum impurity models due to its reduction of the sign problem in real and imaginary time. However, inchworm Monte Carlo is computationally expensive, converging as $1/\sqrt{N}$ where $N$ is the number of samples. We show that the imaginary time integration is amenable to quasi Monte Carlo, with enhanced $1/N$ convergence, by mapping the Sobol low-discrepancy sequence from the hypercube to the simplex with the so-called Root transform. This extends the applicability of the inchworm method to, e.g., multi-orbital Anderson impurity models with off-diagonal hybridization, relevant for materials simulation, where continuous time hybridization expansion Monte Carlo has a severe sign problem.

References in corpus (36)

• Many-Body Physics with Ultracold Gases
• Spins in few-electron quantum dots
• Continuous-time Monte Carlo methods for quantum impurity models
• A continuous-time solver for quantum impurity models
• Strong electronic correlations from Hund's coupling
• Continuous Time Quantum Monte Carlo method for fermions
• Quantum Monte Carlo Impurity Solver for Cluster DMFT and Electronic Structure Calculations in Adjustable Base
• TRIQS: A Toolbox for Research on Interacting Quantum Systems
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
• Exact, Complete, and Universal Continuous-Time Worldline Monte Carlo Approach to the Statistics of Discrete Quantum Systems
• TRIQS/CTHYB: A Continuous-Time Quantum Monte Carlo Hybridization Expansion Solver for Quantum Impurity Problems
• Extended Dynamical Mean Field Theory and GW method
• Taming the dynamical sign problem in real-time evolution of quantum many-body problems
• Nonequilibrium dynamical mean-field calculations based on the non-crossing approximation and its generalizations
• Anomalous superconductivity and its competition with antiferromagnetism in doped Mott insulators
• w2dynamics: Local one- and two-particle quantities from dynamical mean field theory
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• Mott physics and spin fluctuations: a unified framework
• Green's functions from real-time bold-line Monte Carlo: spectral properties of the nonequilibrium Anderson impurity model
• Metal-insulator transition and topological properties of pyrochlore iridates
• Bold Line Diagrammatic Monte Carlo Method: General formulation and application to expansion around the Non-Crossing Approximation
• Phase diagram of pyrochlore iridates: all-in-all-out magnetic ordering and non-Fermi liquid properties
• Green's functions from real-time bold-line Monte Carlo
• Discrete Lehmann representation of imaginary time Green's functions
• Currents and Green's functions of impurities out of equilibrium -- results from inchworm Quantum Monte Carlo
• Mott physics and collective modes: an atomic approximation of the four-particle irreducible functional
• Worm Improved Estimators in Continuous-time Quantum Monte Carlo
• Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions
• Continuous-time Quantum Monte Carlo using Worm Sampling
• Inclusion-Exclusion Principle for Many-Body Diagrammatics
• Multiorbital Quantum Impurity Solver for General Interactions and Hybridizations
• The construction of good lattice rules and polynomial lattice rules
• libdlr: Efficient imaginary time calculations using the discrete Lehmann representation
• A Tensor Train Continuous Time Solver for Quantum Impurity Models
• Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion

Cited by in corpus (4)

• Towards numerically exact computation of conductivity in the thermodynamic limit of interacting lattice models
• Transient Dynamical Phase Diagram of the Spin-Boson Model at Finite Temperature
• Inchworm tensor train hybridization expansion quantum impurity solver
• Automated evaluation of imaginary time strong coupling diagrams by sum-of-exponentials hybridization fitting