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 (11)

• Many-Body Physics with Ultracold Gases
• Continuous-time Monte Carlo methods for quantum impurity models
• Strong electronic correlations from Hund's coupling
• Quantum Monte Carlo Impurity Solver for Cluster DMFT and Electronic Structure Calculations in Adjustable Base
• Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• Bold Line Diagrammatic Monte Carlo Method: General formulation and application to expansion around the Non-Crossing Approximation
• Currents and Green's functions of impurities out of equilibrium -- results from inchworm Quantum Monte Carlo
• Worm Improved Estimators in Continuous-time Quantum Monte Carlo
• 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