# Accelerated Continuous time quantum Monte Carlo method with Machine Learning

## TL;DR

This paper introduces a machine learning-enhanced continuous time quantum Monte Carlo method that significantly speeds up computations while accurately predicting impurity Green's functions and double occupancy at low temperatures.

## Contribution

It combines machine learning with CTQMC to eliminate matrix multiplications, reducing computational time and maintaining accuracy for strongly correlated materials.

## Key findings

- Predicts impurity Green's function accurately at low temperatures
- Reduces computational time compared to conventional CTQMC
- Maintains physical properties at high Matsubara frequencies

## Abstract

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.