Accelerated continuous time quantum Monte Carlo method with machine learning

An acceleration of continuous time quantum Monte Carlo (CTQMC) methods is a potentially interesting branch of work as they are matchless as impurity solvers of a density functional theory in combination with a dynamical mean field theory approach for the description of electronic structures of strongly correlated materials. The inversion of the $k \times k$ matrix given by the diagram expansion order $k$ in the CTQMC update and the multiplication of the $k \times k$ matrix and the non-interacting Green's function to measure the impurity Green's function are computationally time-consuming. Here, we propose the CTQMC method in combination with a machine learning technique, which would eliminate the need for multiplication of the matrix with the non-interacting Green's function. This method predicts the accurate impurity Green's function and double occupancy at low temperature, and also considers the physical properties of high Matsubara frequency in a much shorter computational time than the conventional CTQMC method.