# Quantum Monte Carlo solution of the dynamical mean field equations in real time

## TL;DR

This paper demonstrates that real-time inchworm quantum Monte Carlo methods can effectively solve dynamical mean field equations, enabling accurate non-equilibrium simulations without analytic continuation issues.

## Contribution

The paper introduces a numerically exact real-time Monte Carlo approach for dynamical mean field theory that overcomes the dynamical sign problem and is suitable for time-dependent non-equilibrium problems.

## Key findings

- Successfully applied inchworm Monte Carlo to DMFT on Bethe lattice
- Avoided analytic continuation issues in real-time calculations
- Enabled simulation of far-from-equilibrium dynamics

## Abstract

We present real-time inchworm quantum Monte Carlo results for single-site dynamical mean field theory on an infinite coordination number Bethe lattice. Our numerically exact results are obtained on the L-shaped Keldysh contour and, being evaluated in real-time, avoid the analytic continuation issues typically encountered in Monte Carlo calculations. Our results show that inchworm Monte Carlo methods have now reached a state where they can be used as dynamical mean field impurity solvers and the dynamical sign problem can be overcome. As non-equilibrium problems can be simulated at the same cost, we envisage the main use of these methods as dynamical mean field solvers for time-dependent problems far from equilibrium.