Accelerated continuous time quantum Monte Carlo method with machine learning

초록

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 dynamical mean field theory (DMFT) approach for the description of strongly correlated systems. The inversion of the k x k matrix with k(2) operations given by the diagram expansion order k in the CTQMC fast update and the multiplication of the k x k matrix, and the noninteracting properties with k x omega(m-1)(nmax) operations to measure the in-point correlators, are computationally time consuming. Here we propose the CTQMC method in combination with a machine learning technique, which eliminates the k x omega(nmax) and k x omega(3)(nmax) operations for the two-point impurity Green's functions G(sigma) (i omega(n)) and four-point vertices chi(sigma), ((sigma) over bar) (i omega(n1), i omega(n2), i omega(n3), i omega(n4)), respectively. This method not only predicts the accurate physical properties at low temperature, but also dramatically decreases the computational times of chi(sigma), ((sigma) over bar) (i omega(n1), i omega(n2), i omega(n3), i omega(n4)) for the nonlocal extension of DMFT approximation.