Abstract
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.
Highlights
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
The partition function is expanded in the powers of interaction, and the Monte Carlo simulation is performed by the stochastic sampling of the diagrammatic expansion of interaction terms
In this Rapid Communication, we extend the selflearning Monte Carlo (SLMC) to continuous-time quantum Monte Carlo algorithms for fermion systems
Summary
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. A continuous-time modification of the fermionic QMC algorithm was developed [5,6,7,8] In this algorithm, the partition function is expanded in the powers of interaction, and the Monte Carlo simulation is performed by the stochastic sampling of the diagrammatic expansion of interaction terms. We demonstrate the speedup of SLMC in comparison to the standard CT-AUX, and find the acceleration ratio increases with the average expansion order This Rapid Communication is organized as follows: We first briefly review the CT-AUX algorithm in the Anderson impurity model, after which we give a detailed introduction to the self-learning CT-AUX algorithm, and discuss the physical ideas behind the DGF.
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