Self-Learning Monte Carlo Methods

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. Despite a polynomial complexity in theory (when the model is sign-problem free), one of its bottlenecks is the lack of general and efficient update algorithm, especially for large size systems close to phase transition or with strong frustrations, for which local updates perform badly.

Using the concept of machine learning, we develop a general-purpose update algorithm, dubbed self-learning Monte Carlo (SLMC). In SLMC, an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. The SLMC method has been applied to classical spin models, and various interacting quantum fermionic models, including spin-fermion models, determinant quantum Monte Carlo (DQMC) simulations and dynamical mean-field theory (DMFT) simulations.

In particular, when applied to DQMC simulations, the SLMC method allows us to simulate the universal behavior of interacting bosons and fermions on systems many times larger compared to the conventional methods. This enables us to observe the nontrivial universality class due to the contribution of the fermions.