Self-Learning Monte Carlo Method: Continuous-Time Algorithm

Understand

The recently-introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain.

• We implement this method in the framework of continuous time Monte Carlo method with auxiliary field in quantum impurity models.
• We introduce and train a diagram generating function (DGF) to model the probability distribution of auxiliary field configurations in continuous imaginary time, at all orders of diagrammatic expansion.
• By using DGF to propose global moves in configuration space, we show that the self-learning continuous-time Monte Carlo method can significantly reduce the computational complexity of the simulation.