Self-learning Hybrid Monte Carlo in paradigmatic electron-phonon Hamiltonians

Efficient simulation of many-body Hamiltonians remains a significant challenge in quantum Monte Carlo methods. The self-learning Monte Carlo (SLMC) technique increases efficiency by accelerating simulations and reducing long autocorrelation times through machine learning (ML) models into Monte Carlo update schemes. In this talk, we present our ongoing work extending SLMC methods to the challenging parameter regimes of electron-phonon Hamiltonians. Departing from the original SLMC implementation, we train the ML models to learn costly action derivatives within hybrid Monte Carlo (HMC) simulations. We will discuss the successes achieved and the current challenges faced with this approach and demonstrate its capabilities across representative regions of the phase diagram of the Holstein model.