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Self-learning Monte Carlo method and cumulative update in fermion systems

2017; American Physical Society; Volume: 95; Issue: 24 Linguagem: Inglês

10.1103/physrevb.95.241104

2469-9977

Junwei Liu, Huitao Shen, Yang Qi, Zi Yang Meng, Liang Fu,

Rare-earth and actinide compounds

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.