Self-Learning Monte Carlo Method in Fermion Systems

TL;DR

This paper introduces the self-learning Monte Carlo (SLMC) method tailored for interacting fermion systems, significantly reducing computational costs while maintaining statistical accuracy through a novel cumulative update algorithm.

Contribution

The paper extends the SLMC framework to fermion systems and designs a new cumulative update algorithm that enhances efficiency and reduces complexity.

Findings

SLMC with cumulative update drastically reduces computational cost.

The method remains statistically exact despite efficiency improvements.

Computational complexity is significantly lower than traditional local update algorithms.

Abstract

We develop the self-learning Monte Carlo (SLMC) method, a general-purpose numerical method recently introduced to simulate many-body systems, for studying interacting fermion systems. Our method uses a highly-efficient update algorithm, which we design and dub "cumulative update", to generate new candidate configurations in the Markov chain based on a self-learned bosonic effective model. From general analysis and numerical study of the double exchange model as an example, we find the SLMC with cumulative update drastically reduces the computational cost of the simulation, while remaining statistically exact. Remarkably, its computational complexity is far less than the conventional algorithm with local updates.